Cho lăng trụ tam giác đều A B C . A ' B ' C ' " src="https://img-question-vn.ruangguru.com/ZHIlEYuIfIMW7GeBBuUGw_CdAGx_eGKGl0zSO3DtrSWwsx45qt4Nfm-OjW96EWDnYK2yG5wfnvjnEG-cSoyZPiN53k4Hnv_CWCUC76gSBRZqdg5UdQtJdi_xjUITe2L1VlRQh3DZ" style="width: 84.00px; height: 12.00px; margin-left: 0.00px; margin-top: 4.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="A B C. A apostrophe B apostrophe C apostrophe"> cạnh đáy bằng , góc giữa hai mặt phẳng A ' B C " src="https://img-question-vn.ruangguru.com/OSepzAk3etg9V13u3UQz-N7QfqIUwPXJmIxEAcR0n20D3lczxGo6_R_-YKk8OfNoBPRvltDydIKxJtEORWW_ut5xK99s54HdvkjdadF-3RsSA1h_wS1-_83LuQYlofQyoHVhSi5P" style="width: 48.00px; height: 16.00px; margin-left: 0.00px; margin-top: 2.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="open parentheses A apostrophe B C close parentheses"> và B B ' C C ' " src="https://img-question-vn.ruangguru.com/IP421Txanj3XOsjsJi-zm06tF8hr_UnEMyO822wJ0ouwdu4QWOwQben0uT0fwKyO3bilatIkhiTMzca-PMDhogip1i0V8TYrwmw6jveHJXrJySmzenxPk83Ipzh7cYE4lzf8aZYG" style="width: 52.00px; height: 12.00px; margin-left: 0.00px; margin-top: 4.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="B B apostrophe C C apostrophe"> bằng . Tính thể tích của khối lăng trụ đã cho.

Giải thích

Gọi , M ' " src="https://img-question-vn.ruangguru.com/z6NxofUjpSAK0Fmz2i5FhwXcpbPTSuI8yKT2BLCzpG80YRU0K-6nPKOGfWNtowKdfJn5TyI3Ji4sDgpJkiWYAHDbdyXdm536mJ59_TwZ_FxMZwnsOuqj1Xl4grkYHngtX3QAlN-w" style="width: 20.00px; height: 13.00px; margin-left: 0.00px; margin-top: 3.50px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="begin mathsize 18px style M apostrophe end style"> lần lượt là trung điểm của , B ' C ' " src="https://img-question-vn.ruangguru.com/04AeWhdEE5utepqDm8g6bVutPOq0s1-oeJw1YYkfBZgL7nngkuZsz8x1NnjwwRMhPiN8G6DbN8N3eS4zoIccUPHOaKQQg4tbNQY0WXs3Fu5DW7Bs9nAGusalGz-PcrPHZJ4E6AKo" style="width: 35.00px; height: 13.00px; margin-left: 0.00px; margin-top: 3.50px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="begin mathsize 18px style B apostrophe C apostrophe end style"> . Ta có A ' M M ' , B C ^ " src="https://img-question-vn.ruangguru.com/XALF_CIU0v51dA2-lAvNQenm7yAzNYtVHu0VCgZN0E_ECLp2MtRCZMqu6J2bpF4oUx2nX-qLA2k6Wwy6ZnIKMdwOGW3sbnvIkoK4Z5Al-03-6sILEukHGJ5Y1pIpC9u1GU-eza9o" style="width: 84.00px; height: 20.00px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="stack open parentheses A apostrophe M M apostrophe close parentheses comma B C with hat on top"> và ∆ A ' M M ' " src="https://img-question-vn.ruangguru.com/6kGMVVg5dYnGiyX7XOew5bK2EnHvfu7WrUVGIIA8V4u-_ofdwz6YbfWeI47E7cW5KPtXDC67XvVjognt9WWkoi2_C2G5TyxXVWNsZL9LdD6ybYJPZbyIA3sfRWAdOUnLv0QtFyXm" style="width: 60.00px; height: 12.00px; margin-left: 0.00px; margin-top: 5.11px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="increment A apostrophe M M apostrophe"> vuông tại M ' " src="https://img-question-vn.ruangguru.com/z6NxofUjpSAK0Fmz2i5FhwXcpbPTSuI8yKT2BLCzpG80YRU0K-6nPKOGfWNtowKdfJn5TyI3Ji4sDgpJkiWYAHDbdyXdm536mJ59_TwZ_FxMZwnsOuqj1Xl4grkYHngtX3QAlN-w" style="width: 20.00px; height: 13.00px; margin-left: 0.00px; margin-top: 3.50px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="begin mathsize 18px style M apostrophe end style"> . Do đó góc giữa hai mặt phẳng A ' B C " src="https://img-question-vn.ruangguru.com/OSepzAk3etg9V13u3UQz-N7QfqIUwPXJmIxEAcR0n20D3lczxGo6_R_-YKk8OfNoBPRvltDydIKxJtEORWW_ut5xK99s54HdvkjdadF-3RsSA1h_wS1-_83LuQYlofQyoHVhSi5P" style="width: 48.00px; height: 16.00px; margin-left: 0.00px; margin-top: 2.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="open parentheses A apostrophe B C close parentheses"> và B B ' C C ' " src="https://img-question-vn.ruangguru.com/IP421Txanj3XOsjsJi-zm06tF8hr_UnEMyO822wJ0ouwdu4QWOwQben0uT0fwKyO3bilatIkhiTMzca-PMDhogip1i0V8TYrwmw6jveHJXrJySmzenxPk83Ipzh7cYE4lzf8aZYG" style="width: 52.00px; height: 12.00px; margin-left: 0.00px; margin-top: 4.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="B B apostrophe C C apostrophe"> là A ' M M ' ^ = 30 ° " src="https://img-question-vn.ruangguru.com/gKlUowFZ7L26gXvGYUJjgmAuJ272EfKaFwoLhpOp4gvKHaJ_ztGe7RVx9bipx4KMoJHDRkHWENFtkymVTyNBIifmANjmyWj1UIfrORKGx1fgquDStlXGtUEIHqHzp1G--VrMCGye" style="width: 85.00px; height: 16.00px; margin-left: 0.00px; margin-top: 3.11px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="stack A apostrophe M M apostrophe with hat on top equals 30 degree"> . Mà A ' M ' = a 3 2 ⇒ M M ' = A ' M ' tan 30 ° = 3 a 2 " src="https://img-question-vn.ruangguru.com/xmFi1OXOEHRv6pylCstnZVnZtwOiuEFcm8KLgx7-hNAckQUjPOEgpb4BQJ2mdnSENxWT8lkH_yU7A1ob_l9Jp6BBXxIOABgHSdTJMte_z8-9vEf1cedYoMaGs50wPSKiQnwj-zbX" style="width: 248.00px; height: 40.00px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="A apostrophe M apostrophe equals fraction numerator a square root of 3 over denominator 2 end fraction rightwards double arrow M M apostrophe equals fraction numerator A apostrophe M apostrophe over denominator tan 30 degree end fraction equals fraction numerator 3 a over denominator 2 end fraction"> . Vậy V A B C . A ' B ' C ' = 3 a 2 . a 2 . 3 4 = 3 a 3 3 8 " src="https://img-question-vn.ruangguru.com/-vyM635lsMEKYSPYjIIL1I0IbduPWtGEhLj9RuZDKI54RzIfEepjbypJggzTyNkgbmL3NOemQ_Wezg8zGRRD2xR8XPKDu-g06tBmC87i-nqKZmdYTYnZjNEoptYKfYevp1EndoSg" style="width: 241.33px; height: 40.00px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="V subscript A B C. A apostrophe B apostrophe C apostrophe end subscript equals fraction numerator 3 a over denominator 2 end fraction. a squared. fraction numerator square root of 3 over denominator 4 end fraction equals fraction numerator 3 a cubed square root of 3 over denominator 8 end fraction"> .