{"common":{"save":0,"post_id":"8784","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"10941","post_id":"8784","mon_id":"1159278","chapter_id":"1159334","question":"<p>B\u1ea1n An b\u1ecf m\u1ed9t viên bi \u0111\u1eb7c không th\u1ea5m n\u01b0\u1edbc vào m\u1ed9t cái bình th\u1ee7y tinh ch\u1ee9a n\u01b0\u1edbc có d\u1ea1ng hình tr\u1ee5, bán kính \u0111\u01b0\u1eddng tròn \u0111áy là 1,5 cm. Bi\u1ebft khi viên bi chìm hoàn toàn trong n\u01b0\u1edbc thì n\u01b0\u1edbc trong l\u1ecd dâng lên 0,5 cm. Tính th\u1ec3 tích viên bi mà B\u1ea1n An b\u1ecf vào (l\u1ea5y <span class=\"math-tex\">$\\pi$<\/span> ≈ 3,14, \u0111\u1ed9 dày l\u1ecd không \u0111áng k\u1ec3 và n\u01b0\u1edbc ko thoát ra ngoài).<\/p>","options":["<strong>A.<\/strong> 3,5325 cm³","<strong>B.<\/strong> 3,5352 cm³","<strong>C.<\/strong> 3,3525 cm³","<strong>D.<\/strong> 3,5355 cm³"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> 3,5325 cm³.<\/span><\/p><p>Th\u1ec3 tích c\u1ee7a ph\u1ea7n n\u01b0\u1edbc dâng lên trong bình hình tr\u1ee5 b\u1eb1ng th\u1ec3 tích c\u1ee7a viên bi và b\u1eb1ng<\/p><p><span class=\"math-tex\">$V=\\pi R^2.h=3,14.1,5^2.0,5=3,5325$<\/span> cm³.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-04-16 08:34:31","option_type":"txt","len":2},{"id":"11760","post_id":"8784","mon_id":"1159278","chapter_id":"1159334","question":"<p>M\u1ed9t bình th\u1ee7y tinh hình tr\u1ee5 cao 40 cm, bán kính \u0111áy = 4 dm. Trong bình ch\u1ee9a n\u01b0\u1edbc cao \u0111\u1ebfn 3 dm. H\u1ecfi ph\u1ea3i \u0111\u1ed5 thêm l\u01b0\u1ee3ng n\u01b0\u1edbc vào bình là bao nhiêu \u0111\u1ec3 bình n\u01b0\u1edbc v\u1eeba \u0111\u1ea7y (L\u1ea5y <span class=\"math-tex\">$\\pi$<\/span> ≈ 3,14)?<\/p>","options":["<strong>A.<\/strong> 50,24 lít","<strong>B.<\/strong> 51,83 lít","<strong>C.<\/strong> 58,26 lít","<strong>D.<\/strong> 55,16 lít"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> 50,24 lít.<\/span><\/p><p>\u0110\u1ed5i 40 cm = 4 dm.<\/p><p>Th\u1ec3 tích c\u1ee7a bình th\u1ee7y tinh là <span class=\"math-tex\">$V_t=\\pi R^2h_t=3,14.4^2.4=200,96$<\/span> dm³ = 200,96 lít.<\/p><p>Th\u1ec3 tích c\u1ee7a n\u01b0\u1edbc trong bình lúc \u0111\u1ea7u là <\/p><p><span class=\"math-tex\">$V_n=\\pi R^2h_n=3,14.4^2.3=150,72$<\/span> dm³ = 150,72 lít.<\/p><p>S\u1ed1 lít n\u01b0\u1edbc c\u1ea7n \u0111\u1ed5 thêm \u0111\u1ec3 \u0111\u1ea7y bình là 200,96 – 150,72 = 50,24 lít.<\/p><p>V\u1eady c\u1ea7n ph\u1ea3i \u0111\u1ed5 thêm 50,24 lít thì \u0111\u1ea7y bình.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-05-30 10:24:58","option_type":"txt","len":2},{"id":"11762","post_id":"8784","mon_id":"1159278","chapter_id":"1159334","question":"<p>M\u1ed9t kh\u1ed1i g\u1ed7 hình tr\u1ee5 có chi\u1ec1u cao g\u1ea5p 3 l\u1ea7n \u0111\u01b0\u1eddng kính \u0111áy. Bi\u1ebft di\u1ec7n tích toàn ph\u1ea7n c\u1ee7a kh\u1ed1i g\u1ed7 là <span class=\"math-tex\">$7\\pi$<\/span> m². Tính th\u1ec3 tích c\u1ee7a kh\u1ed1i g\u1ed7 theo \u0111\u01a1n v\u1ecb m³ (l\u1ea5y <span class=\"math-tex\">$\\pi$<\/span> ≈ 3,14 và làm tròn k\u1ebft qu\u1ea3 \u0111\u1ebfn hai ch\u1eef s\u1ed1 th\u1eadp phân).<\/p>","options":["<strong>A.<\/strong> 6,67 m³","<strong>B.<\/strong> 6,66 m³","<strong>C.<\/strong> 6,68 m³","<strong>D.<\/strong> 6,69 m³"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> 6,66 m³.<\/span><\/p><p>Vì chi\u1ec1u cao g\u1ea5p 3 l\u1ea7n \u0111\u01b0\u1eddng kính nên chi\u1ec1u cao g\u1ea5p 6 l\u1ea7n bán kính. T\u1ee9c là <span class=\"math-tex\">$h=6R$<\/span>.<\/p><p>Di\u1ec7n tích toàn ph\u1ea7n c\u1ee7a kh\u1ed1i g\u1ed7 là:<\/p><p><span class=\"math-tex\">$S_{tp}=S_{xq}+2S_\u0111=2\\pi Rh+2\\pi R^2=2\\pi R.6R+2\\pi R^2=14\\pi R^2$<\/span><\/p><p>Hay <span class=\"math-tex\">$14\\pi R^2=7\\pi$<\/span> nên <span class=\"math-tex\">$R=\\dfrac{1}{\\sqrt{2}}$<\/span> m.<\/p><p>Khi \u0111ó <span class=\"math-tex\">$h=6R=6.\\dfrac{1}{\\sqrt{2}}=3\\sqrt{2}$<\/span> m.<\/p><p>Th\u1ec3 tích kh\u1ed1i g\u1ed7 hình tr\u1ee5 là <span class=\"math-tex\">$V=\\pi R^2h=3,14.\\dfrac{1}{2}.3\\sqrt{2}\\approx6,66$<\/span> m³.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-05-30 10:33:57","option_type":"txt","len":1}]}