{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["6"],["9"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" L\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c c\u00f3 _input_ m\u1eb7t, _input_ \u0111\u1ec9nh v\u00e0 _input_ c\u1ea1nh.","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.1.png' \/><\/center>H\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c c\u00f3 $5$ m\u1eb7t, $6$ \u0111\u1ec9nh v\u00e0 $9$ c\u1ea1nh.<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $5;6$ v\u00e0 $9$<\/span><\/span>"}]}],"id_ques":1900},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"],["6"],["10"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" H\u00ecnh ch\u00f3p ng\u0169 gi\u00e1c c\u00f3 _input_ m\u1eb7t, _input_ \u0111\u1ec9nh v\u00e0 _input_ c\u1ea1nh.","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.2.png' \/><\/center>H\u00ecnh ch\u00f3p ng\u0169 gi\u00e1c c\u00f3 $6$ m\u1eb7t, $6$ \u0111\u1ec9nh v\u00e0 $10$ c\u1ea1nh.<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $6;6$ v\u00e0 $10$<\/span><\/span>"}]}],"id_ques":1901},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"H\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng c\u00f3 $6$ m\u1eb7t b\u00ean c\u00f3 bao nhi\u00eau c\u1ea1nh?","select":["A. $6$ c\u1ea1nh","B. $12$ c\u1ea1nh","C. $18$ c\u1ea1nh","D. $24$ c\u1ea1nh"],"hint":"","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.3.png' \/><\/center>H\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng c\u00f3 $6$ m\u1eb7t b\u00ean c\u00f3 $6$ c\u1ea1nh \u1edf \u0111\u00e1y l\u00e0 l\u0103ng tr\u1ee5 \u0111\u1ee9ng l\u1ee5c gi\u00e1c.<br\/>H\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng l\u1ee5c gi\u00e1c c\u00f3 $18$ c\u1ea1nh.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":1902},{"time":24,"part":[{"title":"Ch\u1ecdn <u>nh\u1eefng<\/u> \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn \u0111\u01b0\u1ee3c nhi\u1ec1u \u0111\u00e1p \u00e1n","temp":"checkbox","correct":[["1","3","4","6"]],"list":[{"point":5,"img":"","ques":"Cho h\u00ecnh v\u1ebd, kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u00fang?<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.19.png' \/><\/center>","hint":"","column":2,"number_true":2,"select":["A. $AB\/\/D'C'$","B. $AD\/\/A'C'$","C. $AD \\bot DD'$","D. $mp(ADD'A')\/\/mp(BCC'B')$","E. $mp(ABCD)\/\/mp(ABB'A')$","F. $BC\/\/ mp(ADD'A')$"],"explain":"C\u00e1c kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang l\u00e0 A, C, D v\u00e0 F."}]}],"id_ques":1903},{"time":24,"part":[{"time":3,"title":"Cho h\u00ecnh ch\u00f3p t\u1ee9 di\u1ec7n \u0111\u1ec1u $S.ABCD$, $O$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $AC $ v\u00e0 $ BD$. Ch\u1ee9ng minh r\u1eb1ng $SO\\bot mp(ABCD)$ ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c b\u01b0\u1edbc ch\u1ee9ng minh b\u00e0i to\u00e1n tr\u00ean","temp":"sequence","correct":[[[3],[1],[2],[4]]],"list":[{"point":5,"image":"https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.20.png","left":["T\u01b0\u01a1ng t\u1ef1, ta c\u0169ng c\u00f3: $SO \\bot BD$ ","<span class='basic_left'>Ta c\u00f3, $S.ABCD$ l\u00e0 h\u00ecnh ch\u00f3p t\u1ee9 di\u1ec7n \u0111\u1ec1u n\u00ean: <br\/>$\\Delta SAB=\\Delta SBC=\\Delta SCD=\\Delta SDA \\Leftrightarrow SA=SB=SC=SD$ (l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n t\u1ea1i $S$)<\/span>","<span class='basic_left'>X\u00e9t tam gi\u00e1c $SAC$ c\u00e2n t\u1ea1i $S$ c\u00f3 $OC=OA$, suy ra: $SO \\bot AC$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c c\u00e2n)<br\/>L\u1ea1i c\u00f3, $ABCD$ l\u00e0 h\u00ecnh vu\u00f4ng n\u00ean $OA=OB=OC=OD$.<\/span>","Do v\u1eady, ta c\u00f3: $\\left\\{\\begin{align} &SO\\bot AC\\\\ & SO\\bot BD \\\\ \\end{align}\\right.$ . Suy ra $SO \\bot mp(ABCD)$"],"top":100,"hint":"Ch\u1ee9ng minh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau trong m\u1eb7t ph\u1eb3ng.","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.20.png' \/><\/center>Ta c\u00f3, $S.ABCD$ l\u00e0 h\u00ecnh ch\u00f3p t\u1ee9 di\u1ec7n \u0111\u1ec1u n\u00ean:<br\/> $\\Delta SAB=\\Delta SBC=\\Delta SCD=\\Delta SDA \\Leftrightarrow SA=SB=SC=SD$ (l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n t\u1ea1i $S$)<br\/>L\u1ea1i c\u00f3, $ABCD$ l\u00e0 h\u00ecnh vu\u00f4ng n\u00ean $OA=OB=OC=OD$<br\/>X\u00e9t tam gi\u00e1c $SAC$ c\u00e2n t\u1ea1i $S$ c\u00f3 $OC=OA$, suy ra: $SO \\bot AC$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c c\u00e2n)<br\/>T\u01b0\u01a1ng t\u1ef1, ta c\u0169ng c\u00f3: $SO\\bot BD$<br\/>Do v\u1eady, ta c\u00f3: $\\left\\{\\begin{align} &SO\\bot AC\\\\ & SO\\bot BD \\\\ \\end{align}\\right.$ Suy ra $SO \\bot mp(ABCD)$<br\/><b> Ghi nh\u1edb:<\/b> N\u1ebfu m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1ed9t m\u1eb7t ph\u1eb3ng th\u00ec n\u00f3 vu\u00f4ng g\u00f3c v\u1edbi m\u1ecdi \u0111\u01b0\u1eddng th\u1eb3ng n\u1eb1m trong m\u1eb7t ph\u1eb3ng<\/span>"}]}],"id_ques":1904},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"T\u00ednh di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc nh\u01b0 h\u00ecnh v\u1ebd:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.5.png' \/><\/center>","select":["A. $50\\,cm^2$","B. $100\\,cm^2$","C. $250\\,cm^2$","D. $500\\,cm^2$"],"hint":"H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 chi\u1ec1u cao l\u00e0 $c$, chi\u1ec1u d\u00e0i $a$ v\u00e0 chi\u1ec1u r\u1ed9ng l\u00e0 $b$ th\u00ec c\u00f3 di\u1ec7n t\u00edch xung quanh l\u00e0 $2c(a+b)$","explain":" <span class='basic_left'>Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt l\u00e0:<br\/>$2.10.(10+15)=500\\,(cm^2)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D <\/span><\/span>","column":2}]}],"id_ques":1905},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"T\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc nh\u01b0 h\u00ecnh v\u1ebd:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.6.png' \/><\/center>","select":["A. $4440\\,cm^3$","B. $11100\\,cm^3$","C. $10080\\,cm^3$","D. $15540\\,cm^3$"],"hint":"H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 chi\u1ec1u cao l\u00e0 $c$, chi\u1ec1u d\u00e0i $a$ v\u00e0 chi\u1ec1u r\u1ed9ng l\u00e0 $b$ th\u00ec c\u00f3 th\u1ec3 t\u00edch l\u00e0 $a.b.c\\,$","explain":" <span class='basic_left'>X\u00e9t tam gi\u00e1c $BCC'$ vu\u00f4ng t\u1ea1i $C$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$BC^2+CC'^2=BC'^2\\\\ \\Rightarrow 12^2+CC'^2=37^2\\\\ \\Leftrightarrow CC'^2=1225\\\\ \\Leftrightarrow CC'=35\\,(cm)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt l\u00e0 $12.35.24=10080\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C <\/span><\/span>","column":2}]}],"id_ques":1906},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0110\u00fang ho\u1eb7c Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"H\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 th\u1ec3 t\u00edch l\u00e0 $4096\\,cm^3$ th\u00ec c\u00f3 c\u1ea1nh d\u00e0i $16 cm$. <b>\u0110\u00fang<\/b> hay <b>Sai<\/b>?","select":["\u0110\u00fang","Sai"],"hint":"H\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 c\u1ea1nh d\u00e0i $a cm$ th\u00ec c\u00f3 th\u1ec3 t\u00edch l\u00e0 $a^3 \\,cm^3$.","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.7.png' \/><\/center><br\/>Ta c\u00f3 $16^3=4096$. <br\/>Do v\u1eady h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 th\u1ec3 t\u00edch l\u00e0 $4096\\,cm^3$ th\u00ec c\u00f3 c\u1ea1nh d\u00e0i $16\\,cm$<br\/><span class='basic_pink'>V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0111\u00fang.<\/span><br\/><\/span>","column":2}]}],"id_ques":1907},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt $ABCD.A'B'C'D'$ \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh $8\\,cm$. T\u00ednh th\u1ec3 t\u00edch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, bi\u1ebft $AC'^2=228$.","select":["A. $64\\,cm^3$","B. $640\\,cm^3$","C. $640\\sqrt{2}\\,cm^3$","D. $1280\\,cm^3$"],"hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago v\u00e0o tam gi\u00e1c $AA'C'$ \u0111\u1ec3 t\u00ednh chi\u1ec1u cao h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt.","explain":" <span class='basic_left'><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.8.png' \/><\/center>V\u00ec $ABCD.A'B'C'D'$ l\u00e0 h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng n\u00ean $A'B'=B'C'=C'D'=A'D'$<br\/>X\u00e9t tam gi\u00e1c $A'B'C'$ vu\u00f4ng c\u00e2n t\u1ea1i $B'$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3: $A'B'^2+B'C'^2=A'C'^2\\\\ \\Rightarrow 8^2+8^2=A'C'^2\\\\ \\Leftrightarrow A'C'=8\\sqrt{2}\\,(cm)$<br\/>X\u00e9t tam gi\u00e1c $AA'C'$ vu\u00f4ng t\u1ea1i $A'$<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago, ta c\u00f3:<br\/>$AA'^2+A'C'^2=AC'^2\\\\ \\Rightarrow AA'^2+(8\\sqrt{2})^2=228\\\\ \\Leftrightarrow AA'^2=100\\\\ \\Leftrightarrow AA'=10\\,(cm)$<br\/>V\u1eady th\u1ec3 t\u00edch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt l\u00e0 $10.8.8=640\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":1908},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["25"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a m\u1ed9t h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n b\u1eb1ng di\u1ec7n t\u00edch xung quanh c\u1ee7a m\u1ed9t h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 chi\u1ec1u d\u00e0i l\u00e0 $40cm$, chi\u1ec1u r\u1ed9ng l\u00e0 $35cm$ v\u00e0 chi\u1ec1u cao l\u00e0 $25cm$.<br\/><b> Tr\u1ea3 l\u1eddi:<\/b> _input_($cm$)","hint":"","explain":"<span class='basic_left'>Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt l\u00e0 $2.25.(35+40)=3750\\,(cm^2)$<br\/>Do \u0111\u00f3, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0 $3750\\,cm^2$<br\/>Di\u1ec7n t\u00edch m\u1ed9t m\u1eb7t c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0 $3750:6=625\\,(cm^2)$<br\/>V\u1eady \u0111\u1ed9 d\u00e0i m\u1ed9t c\u1ea1nh c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0 $\\sqrt{625}=25\\,(cm)$<br\/>Suy ra h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 c\u1ea1nh d\u00e0i $25\\,cm$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $25$<\/span><\/span>"}]}],"id_ques":1909},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c, \u0111\u00e1y l\u00e0 tam gi\u00e1c vu\u00f4ng c\u00e2n c\u00f3 c\u1ea1nh huy\u1ec1n l\u00e0 $8\\, cm$ v\u00e0 chi\u1ec1u cao l\u00e0 $10\\sqrt{2}\\,cm$.","select":["A. $160\\sqrt{2}\\,cm^3$","B. $160\\,cm^3$","C. $320\\sqrt{2}\\,cm^3$","D. $320\\,cm^3$"],"hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago t\u00ednh \u0111\u1ed9 d\u00e0i m\u1ed7i c\u1ea1nh c\u1ee7a tam gi\u00e1c vu\u00f4ng c\u00e2n.","explain":" <span class='basic_left'>X\u00e9t h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c $ABC.A'B'C'$ c\u00f3 \u0111\u00e1y $ABC$ vu\u00f4ng c\u00e2n t\u1ea1i $A$ v\u00e0 $A'B'C'$ vu\u00f4ng c\u00e2n t\u1ea1i $A'$.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.9.png' \/><\/center>X\u00e9t \u0111\u00e1y l\u00e0 tam gi\u00e1c $ABC$ vu\u00f4ng c\u00e2n t\u1ea1i $A$.<br\/>Ta c\u00f3: $AB=AC$ (t\u00ednh ch\u1ea5t tam gi\u00e1c vu\u00f4ng c\u00e2n)<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$AB^2+AC^2=BC^2\\\\ \\Rightarrow 2AB^2=64\\\\ \\Leftrightarrow AB^2=32\\\\ \\Leftrightarrow AB=4\\sqrt{2}\\,(cm)$<br\/>V\u1eady $AC=AB=4\\sqrt{2}\\,cm$<br\/>Di\u1ec7n t\u00edch \u0111\u00e1y $ABC$ l\u00e0 $\\dfrac{1}{2}.AC.AB=\\dfrac{1}{2}.4\\sqrt{2}.4\\sqrt{2}=16\\,(cm^2)$<br\/>V\u1eady th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c l\u00e0 $10\\sqrt{2}.16=160\\sqrt{2}\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":1910},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"T\u00ednh th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng c\u00f3 chi\u1ec1u cao $10 cm$, \u0111\u00e1y l\u00e0 tam gi\u00e1c c\u00f3 $3$ c\u1ea1nh l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng $9 cm,\\, 40 cm$ v\u00e0 $41 cm$.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.10.png' \/><\/center>","select":["A. $180\\,cm^3$","B. $820\\,cm^3$","C. $1800\\,cm^3$","D. $8200\\,cm^3$"],"hint":"X\u00e9t \u0111\u00e1y l\u00e0 tam gi\u00e1c g\u00ec?","explain":" <span class='basic_left'>Ta c\u00f3: $9^2+40^2=1681=41^2$<br\/>Theo \u0111\u1ecbnh l\u00fd Pytago \u0111\u1ea3o, $9 cm,\\, 40 cm$ v\u00e0 $41 cm$ l\u00e0 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a tam gi\u00e1c vu\u00f4ng. <br\/>Khi \u0111\u00f3, \u0111\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng l\u00e0 $9\\,cm$ v\u00e0 $40\\,cm$<br\/>V\u1eady di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0 $\\dfrac{1}{2}.9.40=180\\,(cm^2)$<br\/>Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng l\u00e0 $10.180=1800\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":1911},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["120120"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng v\u1edbi k\u00edch th\u01b0\u1edbc trong h\u00ecnh sau:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.11.png' \/><\/center><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_ ($cm^3$)","hint":"T\u00ednh c\u1ea1nh g\u00f3c vu\u00f4ng c\u00f2n l\u1ea1i c\u1ee7a \u0111\u00e1y.","explain":" <span class='basic_left'>X\u00e9t tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $B$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$AB^2+BC^2=AC^2\\\\ \\Rightarrow 33^2+BC^2=65^2\\\\ \\Leftrightarrow BC^2=3136\\\\ \\Leftrightarrow BC=56\\,(cm)$<br\/>Di\u1ec7n t\u00edch \u0111\u00e1y $ABC$ l\u00e0 $\\dfrac{1}{2}.56.33=924\\,(cm^2)$<br\/>V\u1eady th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng l\u00e0 $130.924=120120\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $120120$<\/span><\/span>"}]}],"id_ques":1912},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o \u00f4 tr\u1ed1ng","title_trans":" K\u1ebft qu\u1ea3 \u0111\u1ec3 d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n","temp":"fill_the_blank","correct":[[["115,6"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng v\u1edbi k\u00edch th\u01b0\u1edbc trong h\u00ecnh sau:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.12.png' \/><\/center><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_ ($cm^3$)<br\/>","hint":"T\u00ednh c\u1ea1nh g\u00f3c vu\u00f4ng c\u00f2n l\u1ea1i c\u1ee7a \u0111\u00e1y.","explain":"<span class='basic_left'><br\/><span class='basic_green'> H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> T\u00ednh $AC$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c v\u00e0 di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ednh di\u1ec7n t\u00edch \u0111\u00e1y.<br\/><b>B\u01b0\u1edbc 4:<\/b> T\u00ednh th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>\u0110\u00e1y h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng \u0111\u01b0\u1ee3c gh\u00e9p b\u1edfi tam gi\u00e1c vu\u00f4ng $ABC$ v\u00e0 h\u00ecnh ch\u1eef nh\u1eadt $BCMN$<br\/>X\u00e9t tam gi\u00e1c vu\u00f4ng $ABC$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$BC^2=AB^2+AC^2\\\\ \\Rightarrow 5^2=3^2+AC^2\\\\ \\Leftrightarrow AC^2=16\\\\ \\Leftrightarrow AC=4\\,(cm)$<br\/>Di\u1ec7n t\u00edch tam gi\u00e1c $ABC$ l\u00e0 $\\dfrac{1}{2}.3.4=6\\,(cm^2)$<br\/>Di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt $BCMN$ l\u00e0 $5.2,2=11\\,(cm^2)$<br\/>Di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0 $6+11=17\\,(cm^2)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng l\u00e0 $17.6,8=115,6\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $115,6$<\/span><\/span>"}]}],"id_ques":1913},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"select":["A. $54\\sqrt{3}$","B. $51\\sqrt{3}$","C. $53\\sqrt{3}$"],"ques":"Cho h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c \u0111\u1ec1u c\u00f3 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n l\u1edbn h\u01a1n di\u1ec7n t\u00edch xung quanh l\u00e0 $18\\sqrt{3} cm^2$. Chi\u1ec1u cao b\u1eb1ng \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a tam gi\u00e1c \u1edf \u0111\u00e1y. T\u00ednh th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b> ?($cm^3$)","hint":"\u0110\u1eb7t \u0111\u1ed9 d\u00e0i c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c \u1edf \u0111\u00e1y l\u00e0 $x$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago t\u00ednh \u0111\u1ed9 d\u00e0i m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng.","explain":" <span class='basic_left'><span class='basic_left'><br\/><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> T\u00ednh di\u1ec7n t\u00edch \u0111\u00e1y<br\/><b>B\u01b0\u1edbc 2:<\/b> \u0110\u1eb7t \u0111\u1ed9 d\u00e0i \u0111\u00e1y l\u00e0 $x$.<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ednh $x$ r\u1ed3i suy ra chi\u1ec1u cao.<br\/><b>B\u01b0\u1edbc 4:<\/b> T\u00ednh th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng .<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.13.png' \/><\/center>Ta c\u00f3: $S_{tp}=S_{xq}+2S_{\u0111}\\Rightarrow S_{\u0111}=\\dfrac{S_{tp}-S_{xq}}{2}$<br\/>Do v\u1eady di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0 $9\\sqrt{3}\\,cm^2$<br\/>G\u1ecdi \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a tam gi\u00e1c \u1edf \u0111\u00e1y l\u00e0 $x\\,(cm)$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.13a.png' \/><\/center>Theo \u0111\u1ecbnh l\u00fd Pytago, ta c\u00f3:<br\/>Chi\u1ec1u cao t\u01b0\u01a1ng \u1ee9ng v\u1edbi c\u1ea1nh c\u1ee7a tam gi\u00e1c \u1edf \u0111\u00e1y l\u00e0 $\\sqrt{x^2-\\left(\\dfrac{x}{2}\\right)^2}=\\dfrac{x\\sqrt{3}}{2}\\,(cm)$<br\/>V\u00ec di\u1ec7n t\u00edch tam gi\u00e1c \u1edf \u0111\u00e1y l\u00e0 $9\\sqrt{3}\\,cm^2$ n\u00ean ta c\u00f3: <br\/>$\\dfrac{1}{2}.x.\\dfrac{x\\sqrt{3}}{2}=9\\sqrt{3}\\\\ \\Leftrightarrow \\dfrac{x^2\\sqrt{3}}{4}=9\\sqrt{3}\\\\ \\Leftrightarrow x^2=36\\\\ \\Leftrightarrow x=6\\,(cm)$<br\/>V\u1eady \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y l\u00e0 $6\\,cm$. Do \u0111\u00f3, chi\u1ec1u cao c\u1ee7a l\u0103ng tr\u1ee5 \u0111\u1ee9ng l\u00e0 $6\\,cm$<br\/>V\u1eady th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng l\u00e0 $6.9\\sqrt{3}=54\\sqrt{3}\\,(cm^3)$<\/span>"}]}],"id_ques":1914},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0110\u00fang ho\u1eb7c Sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"H\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u $S.ABCD$ c\u00f3 \u0111\u1ed9 d\u00e0i trung \u0111o\u1ea1n l\u00e0 $40\\,cm$ v\u00e0 c\u1ea1nh \u0111\u00e1y l\u00e0 $25\\,cm$ th\u00ec c\u00f3 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n l\u00e0 $4000 cm^2$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.14.png' \/><\/center>","select":["\u0110\u00fang","Sai"],"hint":"","explain":" <span class='basic_left'>Di\u1ec7n t\u00edch \u0111\u00e1y $ABCD$ l\u00e0 $BC^2=25^2=625\\,(cm^2)$<br\/>Di\u1ec7n t\u00edch xung quanh l\u00e0 $2.AB.SH=2.25.40=2000\\,(cm^2)$<br\/>Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n l\u00e0 $2000+625=2625\\,(cm^2)$<br\/><span class='basic_pink'>V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 sai.<\/span><\/span>","column":2}]}],"id_ques":1915},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai","temp":"fill_the_blank","correct":[[["3707,53"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"Cho h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u c\u00f3 chu vi \u0111\u00e1y l\u00e0 $150\\,cm$, \u0111\u1ed9 d\u00e0i trung \u0111o\u1ea1n l\u00e0 $35$ $cm$. Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0:<br\/><b> \u0110\u00e1p s\u1ed1: <\/b>_input_ ($cm^2$)<br\/>","hint":"T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y r\u1ed3i t\u00ednh di\u1ec7n t\u00edch \u0111\u00e1y.","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.15a.png' \/><\/center>H\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c \u0111\u1ec1u.<br\/>Do v\u1eady \u0111\u1ed9 d\u00e0i m\u1ed7i c\u1ea1nh c\u1ee7a tam gi\u00e1c l\u00e0 $50\\,cm$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.15.png' \/><\/center>X\u00e9t tam gi\u00e1c $ABC$ \u0111\u1ec1u c\u00f3 c\u1ea1nh d\u00e0i $50\\,cm$ \u0111\u01b0\u1eddng cao $AH$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago v\u00e0o tam gi\u00e1c vu\u00f4ng $AHB$ ta c\u00f3:<br\/>$AH^2+HB^2=AB^2\\\\ \\Rightarrow AH^2+25^2=50^2\\\\ \\Leftrightarrow AH^2=1875\\\\ \\Leftrightarrow AH=25\\sqrt{3}\\,(cm)$<br\/>V\u1eady di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0 $\\dfrac{1}{2}AH.BC=\\dfrac{1}{2}.25\\sqrt{3}.50=625\\sqrt{3}\\,(cm^2)$<br\/>Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p b\u1eb1ng $p.h=\\dfrac{150}{2}.35=2625\\,(cm^2)$<br\/>($p$ n\u1eeda chu vi \u0111\u00e1y, $h$ l\u00e0 chi\u1ec1u cao)<br\/>V\u1eady di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh ch\u00f3p b\u1eb1ng $S_{xq}+S_{\u0111}=2625+625\\sqrt{3}=3707,53\\,(cm^2)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $3707,53$<\/span><\/span>"}]}],"id_ques":1916},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"T\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 k\u00edch th\u01b0\u1edbc nh\u01b0 h\u00ecnh v\u1ebd:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.16.png' \/><\/center>","select":["A. $541,44 \\,cm^3$","B. $1802,88\\,cm^3$","C. $1082,88 \\,cm^3$","D. $3248,64 \\,cm^3$"],"hint":"","explain":"<span class='basic_left'><br\/>- V\u00ec $S.ABCD$ l\u00e0 ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u n\u00ean $ABCD$ l\u00e0 h\u00ecnh vu\u00f4ng v\u00e0 c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n.<br\/>+) $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$<br\/>+) $O$ giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng ch\u00e9o.<br\/>- V\u00ec $SO$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean $SO \\bot mp(ABCD) \\,\\Rightarrow SO\\bot HO$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.16.png' \/><\/center>Ta c\u00f3: $AH=\\dfrac{AB}{2}=\\dfrac{16}{2}=8\\,(cm)$<br\/>X\u00e9t tam gi\u00e1c $SAH$ vu\u00f4ng t\u1ea1i $H$ c\u00f3 $SA=17\\,cm$ v\u00e0 $AH=8\\,cm$<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$SA^2=SH^2+AH^2\\\\ \\Rightarrow SH^2=17^2-8^2\\\\ \\Leftrightarrow SH^2=225\\\\ \\Leftrightarrow SH=15\\,(cm)$<br\/>Ta c\u00f3, $HA=HB;\\,OA=OC$, suy ra $HO$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c $ABC$.<br\/>Suy ra $HO=\\dfrac{BC}{2}=8\\,cm$<br\/>X\u00e9t tam gi\u00e1c $SOH$ vu\u00f4ng t\u1ea1i $O$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$SO^2=SH^2-OH^2\\\\ \\Rightarrow SO^2=15^2-8^2\\\\ \\Leftrightarrow SO^2=161\\\\ \\Leftrightarrow SO\\approx 12,69\\,(cm)$<br\/>Di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng $ABCD$ l\u00e0 $16^2=256\\,(cm^2)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p $S.ABCD$ l\u00e0 $\\dfrac{1}{3}. SO. S_{ABCD}=\\dfrac{1}{3}.12,69.256=1082,88\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":1917},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["10752"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u, c\u00f3 c\u1ea1nh \u0111\u00e1y l\u00e0 $32 cm$ v\u00e0 chi\u1ec1u cao b\u1eb1ng $36 cm$. C\u1eaft h\u00ecnh ch\u00f3p b\u1edfi m\u1eb7t ph\u1eb3ng \u0111i qua c\u00e1c trung \u0111i\u1ec3m c\u1ea1nh b\u00ean. T\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p c\u1ee5t \u0111\u01b0\u1ee3c h\u00ecnh th\u00e0nh.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_ ($cm^3$)","hint":"Th\u1ec3 t\u00edch ch\u00f3p c\u1ee5t b\u1eb1ng th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p l\u1edbn tr\u1eeb \u0111i th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p nh\u1ecf","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.17.png' \/><\/center>X\u00e9t h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u $S.ABCD$.<br\/>Gi\u1ea3 s\u1eed m\u1eb7t ph\u1eb3ng c\u1eaft c\u00e1c c\u1ea1nh b\u00ean $SA;SB;SC;SD$ v\u00e0 $SO$ l\u1ea7n l\u01b0\u1ee3t t\u1ea1i $A';B';C';D'$ v\u00e0 $O'$<br\/>V\u00ec m\u1eb7t ph\u1eb3ng \u0111i qua c\u00e1c trung \u0111i\u1ec3m c\u1ea1nh b\u00ean n\u00ean $A';B';C'$ v\u00e0 $D'$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh $SA;SB;SC$ v\u00e0 $SD$<br\/>Khi \u0111\u00f3 ta c\u00f3: $A'B'; B'C';C'D'$ v\u00e0 $D'A'$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a c\u00e1c tam gi\u00e1c $SAB$, $SBC$, $SCD$ v\u00e0 $SDA$.<br\/>Suy ra $A'B'=B'C'=C'D'=D'A'=\\dfrac{AB}{2}=16\\,cm$<br\/>V\u00ec v\u1eady \u0111\u00e1y nh\u1ecf l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh $16\\,cm$.<br\/>Ta c\u0169ng c\u00f3 $O'$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $SO$.<br\/>Do \u0111\u00f3, $SO'=\\dfrac{1}{2}SO=18\\,cm$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p $S.ABCD$ l\u00e0 $\\dfrac{1}{3}.SO.S_{ABCD}=\\dfrac{1}{3}.36.32^2=12288\\,(cm^3)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p $S.A'B'C'D'$ l\u00e0 $\\dfrac{1}{3}.SO'.S_{A'B'C'D'}=\\dfrac{1}{3}.18.16^2=1536\\,(cm^3)$<br\/>V\u1eady th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t l\u00e0 $12288-1536=10752\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 ph\u1ea3i \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $10752$<\/span><\/span>"}]}],"id_ques":1918},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho h\u00ecnh ch\u00f3p c\u1ee5t t\u1ee9 gi\u00e1c \u0111\u1ec1u $ABCD.A\u2019B\u2019C\u2019D\u2019$ c\u00f3 c\u1ea1nh b\u00ean l\u00e0 $8a$; c\u1ea1nh \u0111\u00e1y l\u1edbn b\u1eb1ng $10a$ v\u00e0 \u0111\u00e1y nh\u1ecf b\u1eb1ng $6a$. T\u00ednh di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t \u0111\u00f3.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.18.png' \/><\/span>","select":["A. $S_{xq}=64a^2\\sqrt{15}$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","B. $S_{xq}=28a^2\\sqrt{15}$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","C. $S_{xq}=64a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","D. $S_{xq}=28a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)"],"hint":"K\u1ebb trung \u0111o\u1ea1n $A'H$","explain":"<span class='basic_left'>X\u00e9t m\u1eb7t b\u00ean $AA'B'B$, k\u1ebb $A'H\\bot AB$.<br\/>Ta c\u00f3 $AH=\\dfrac{AB-A'B'}{2}=\\dfrac{10a-6a}{2}=2a$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai23/lv1/img\/H8_B23_D1.18a.png' \/><\/center>X\u00e9t tam gi\u00e1c $A'AH$ vu\u00f4ng t\u1ea1i $H$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$AA'^2=AH^2+A'H^2\\\\ \\Rightarrow A'H^2=64a^2-4a^2\\\\ \\Leftrightarrow A'H=2a\\sqrt{15}$<br\/>V\u1eady di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t l\u00e0:<br\/> $4S_{AA'B'B}=4.\\dfrac{A'B'+AB}{2}.A'H=4.\\dfrac{6a+10a}{2}.2a\\sqrt{15}=64a^2\\sqrt{15}$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":1919}],"lesson":{"save":0,"level":1}}