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Giải bài 14 trang 77 sách bài tập toán 8 - Cánh diều

Cho hai hình chóp tứ giác đều \(S.ABCD\) và \(S.A'B'C'D'\) lần lượt có chiều cao \(SO\) và \(SO'\). Biết \(AB = 2a,A'B' = 3a,SO = 2b,SO' = 3b\) (Hình 12).

ꦉTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Cho hai hình chóp tứ giác đều \(S.ABCD\) và \(S.A'B'C'D'\) lần lượt có chiều cao \(SO\) và \(SO'\). Biết \(AB = 2a,A'B' = 3a,SO = 2b,SO' = 3b\) (Hình 12). Tính tỉ số thể tích của hình chóp tứ giác đều \(S.ABCD\) và \(S.A'B'C'D'\) biết rẳng \(a\) và \(b\) cùng đơn vị đo.

 

Phương pháp giải - Xem chi tiết

Áp dụng công thức tính thể tích của hình chóp tứ giác đều: \(V = \frac{1}{3}.S.h\), trong đó \(V\) là thể tích, \(S\) là diện tích đáy, \(h\) là chiều cao của hình chóp tứ giác đều. Sau đó tính tỉ số thể tích của hai hình chóp tứ giác đều đó.

Lời giải chi tiết

Thể tích của hình chóp tứ giác đều \(S.ABCD\) là:\(\frac{1}{3}.\left( {2a.2a} \right).2b = \frac{{8{a^2}b}}{3}\) (đơn vị thể tích)Thể tích của hình chóp tứ giác đều \(S.A'B'C'D'\) là:\(\frac{1}{3}.\left( {3a.3a} \right).3b = 9{a^2}b\) (đơn vị thể tích)Tỉ số thể tích của hình chóp tứ giác đều \(S.ABCD\) và \(S.A'B'C'D'\) là:\(\frac{{8{a^2}b}}{3}:\left( {9{a^2}b} \right) = \frac{8}{{27}}\)

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