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Giải Bài 4 trang 63 sách bài tập toán 7 tập 1 - Chân trời sáng tạo

Một chi tiết máy bằng thép hình lăng trụ đứng tứ giác có đáy là một hình thoi có độ dài hai đường chéo là 16 cm và 18 cm, chiều cao 10 cm. Người ta khoét một lỗ hình hộp chữ nhật (Hình 9) có kích thước hai cạnh đáy là 2 cm và 6 cm. Tính thể tích còn lại của khối thép.

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Đề bài

ꦬMột chi tiết máy bằng thép hình lăng trụ đứng tứ giác có đáy là một hình thoi có độ dài hai đường chéo là 16 cm và 18 cm, chiều cao 10 cm. Người ta khoét một lỗ hình hộp chữ nhật (Hình 9) có kích thước hai cạnh đáy là 2 cm và 6 cm. Tính thể tích còn lại của khối thép.

 

Lời giải chi tiết

Diện tích đáy hình thoi của khối lăng trụ là: Sđ = \(\dfrac{1}{2}\). 16 . 18 = 144 (cm2).

Thể tích của hình lăng trụ có đáy là hình thoi là: V = 144 . 10 = 1 440 (cm3).

Lỗ hình hộp chữ nhật có kích thước hai cạnh đáy là 2 cm và 6 cm và chiều cao chính bằng chiều cao của hình lăng trụ có đáy là hình thoi và là 10 cm. Do đó, thể tích cái lỗ hình hộp chữ nhật là:

Vl = 2 . 6 . 10 = 120 (cm3).

Thể tích còn lại của khối thép là: Vcl = V – Vl = 1 440 – 120 = 1 320 (cm3) 

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