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Giải bài 10.22 trang 102 SGK Toán 7 tập 2 - Kết nối tri thức

Người ta xếp một số viên gạch dạng hình hộp chữ nhật tạo thành một khối hình lập phương cạnh 20 cm như hình 10.44. a) Tính diện tích xung quanh và diện tích toàn phần của khối hình lập phương. b) Tìm kích thước mỗi viên gạch.

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Đề bài

Người ta xếp một số viên gạch dạng hình hộp chữ nhật tạo thành một khối hình lập phương cạnh 20 cm như hình 10.44. a) Tính diện tích xung quanh và diện tích toàn phần của khối hình lập phương. b) Tìm kích thước mỗi viên gạch.

Phương pháp giải - Xem chi tiết

Cạnh a = 20 cm a)

Sxq = Cđáy.h = 4a.a = 4a2

Stp = Sxq + 2Sđáy = 4a2 + 2a2 = 6a2

Lời giải chi tiết

a)Diện tích xung quanh khối gạch hình lập phương là :

 4 . 202 = 1600 (cm2)

Diện tích toàn phần của khối gạch hình lập phương là: \({6.20^2} = 2400\left( {c{m^2}} \right)\)b) Theo hình vẽ ta ta có:Chiều rộng của viên gạch hình hộp chữ nhật bằng \(\dfrac{1}{2}\) cạnh hình lập phươngChiều rộng của hình hộp chữ nhật là: 20 : 2=10 (cm)                 Chiều cao của viên gạch bằng \(\dfrac{1}{4}\) cạnh hình lập phương Chiều cao của viên gạch là:20 : 4 = 5 (cm)Vậy mỗi viên gạch có kích thước là: chiều dài 20cm, chiều rộng 10cm, chiều cao 5cm 

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