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Giải bài 24 trang 79 sách bài tập toán 8 - Cánh diều

Cho một hình chóp tứ giác đều có độ dài cạnh đáy bằng chiều cao.

🍃Tổng 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 một hình chóp tứ giác đều có độ dài cạnh đáy bằng chiều cao. Chứng minh thể tích của hình chóp tứ giác đều đó bằng một phần ba thể tích của hình lập phương có độ dài cạnh bằng độ dài cạnh đáy của hình chóp tứ giác đều đó.

Phương pháp giải - Xem chi tiết

Áp dụng công thức \(V = \frac{1}{3}.S.h\), trong đó \(V\) là thể tích \(S\) là diện tích đáy, \(h\) là chiều cao của hình chóp tứ giác đều. 𓂃Và công thức tính diện tích của hình lập phương \(S = {a^3}\).

Lời giải chi tiết

Gọi độ dài cạnh đáy và chiều cao của hình chóp tứ giác đều là \(a\left( {a > 0} \right)\).Do hình lập phương có độ dài cạnh bằng độ dài cạnh đáy của hình chóp tứ giác đều nên độ dài cạnh của hình lập phương là \(a\).Thể tích của hình chóp tứ giác đều là: \(\frac{1}{3}.{a^2}.a = \frac{1}{3}.{a^3}\)Thể tích của hình lập phương là \({a^3}\)Vậy thể tích của hình chóp tứ giác đều bằng một phần ba thể tích của hình lập phương.

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