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Bài 8.32 trang 83 SGK Toán 11 tập 2 - Cùng khám phá

Một khối hộp chữ nhật làm từ kim loại rắn có đáy hình chữ nhật kích thước 48 cm x 25 cm
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Đề bài

Một khối hộp chữ nhật làm từ kim loại rắn có đáy hình chữ nhật kích thước 48 cm x 25 cm. Khối kim loại này sau đó được nung chảy và đúc lại thành khối chóp đáy hình vuông với độ cao không đổi. Tìm độ dài cạnh đáy của khối chóp này.

Phương pháp giải - Xem chi tiết

Công thức tính thể tích hình hộp chữ nhật: \(V = abc\) với a là chiều dài đáy, b là chiều rộng đáy, c là chiều cao. Công thức tính thể tích hình chóp là: \(V = \frac{1}{3}S.h\) với S là diện tích đáy, h là chiều cao.

Lời giải chi tiết

Gọi chiều cao của khối hộp chữ nhật là h

Thể tích khối hộp chữ nhật là: \(V = 48.25.h = 1200.h\) (cm3)

Gọi độ dài đáy khối chóp là a (cm)Ta có:\(\begin{array}{l}1200.h = \frac{1}{3}.S.h\\ \Leftrightarrow S = 3600\\ \Leftrightarrow {a^2} = 3600\\ \Leftrightarrow a = 60\end{array}\)Vậy cạnh đáy của khối chóp dài 60cm.

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