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Giải Bài 5 trang 11 SGK Toán 8 tập 1 – Chân trời sáng tạo

Viết biểu thức biểu thị thể tích (V) và diện tích xung quanh (S) của hình hộp chữ nhật trong Hình (5). Tính giá trị của (V), (S) khi (x = 4)cm; (y = 2)cm và (z = 1)cm.

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Đề bài

Viết biểu thức biểu thị thể tích \(V\) và diện tích xung quanh \(S\) của hình hộp chữ nhật trong Hình \(5\). Tính giá trị của \(V\), \(S\) khi \(x = 4\)cm; \(y = 2\)cm và \(z = 1\)cm.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a) Công thức tính thể tích và diện tích xung quanh của hình hộp chữ nhật:

\(V = a.b.h\)

\(S = \left( {a + b} \right).2.h\)

Trong đó \(V\), \(S\), \(a\), \(b\), \(h\) lần lượt là thể tích, diện tích xung quanh, chiều dài, chiều rộng, chiều cao của hình hộp chữ nhật. b) Tính giá trị biểu thức \(V\), \(S\) khi \(x = 4\)cm; \(y = 2\)cm và \(z = 1\)cm.

Lời giải chi tiết

a) Ta có:\(V = 3x.4y.2z = \left( {3.4.2} \right).xyz = 24xyz\)\(S = \left( {3x + 4y} \right).2.2z = \left( {3x + 4y} \right).4z\)b) Thay \(x = 4\)cm; \(y = 2\)cm và \(z = 1\)cm vào các biểu thức \(V\), \(S\) ta có:\(V = 24.4.2.1 = 192\) (\(c{m^3}\))\(S = \left( {3.4 + 4.2} \right).4.1 = 20.4 = 80\) (\(c{m^2}\)) 

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