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Giải Bài 8 trang 57 sách bài tập toán 7 tập 1 - Chân trời sáng tạo

Hai hình hộp chữ nhật được ghép với nhau như Hình 11. a) Tính thể tích của khối ghép. b) Tính diện tích toàn phần của khối ghép.

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Đề bài

Hai hình h🦋ộp chữ nhật được ghép với nhau như Hình 11.

a) Tính thể tích của khối ghép.

b) Tính diện tích toàn phần của khối ghép.

 

Phương pháp giải - Xem chi tiết

൩a) Ta tính thể tích của từng hình hộp chữ nhật. Tổng của chúng là thể tích của khối ghép.

Thể tích hình hộp chữ nh𓂃ật có kích thước a,b,c là: V= a.b.c

b) Ta tính diện tích toàn phần của 2 hộp rồi tr🥂ừ đi 2 lần diện tích phần tiếp xúc nhau

Diện tích toàn phần hình hộp chữ nhật có chiều rộng a, chiều dài b, chiều cao c là: \(S = S_{xq}+S_{đáy}=2.(a+b).c + 2.a.b\)  

Lời giải chi tiết

a) Khối hộp 🧸chữ nhật phía sau có kích thước 10 in, 2 in, 9 in nên c🙈ó thể tích là:

V1 = 10 . 2 . 9 = 180 (in3).

Khối hộp chữ nhật phía trước có kích thước 6 🐼in, 2 in, 9 in nên có th🐓ể tích là:

V2 = 6 . 2 . 9 = 108 (in3).

Hai khối hộp chữ nhật được ghép lại ൲như Hình 11 có thể tích là:

V = V1 + V2 = 180 + 108 = 288 (in3).

b) Diện tích toàn phần của khối ghép bằng tổng diện tích toàn phần của hai khối ൩🐈trừ đi hai lần diện tích mặt tiếp xúc nhau.

Diện tích toàn phần của khối hộp chữ nhật bằng tổng diện tích xung quanh và diện tích 2 🍎đáy.

Diện tích toàn 🥃ph𒐪ần của khối hộp chữ nhật phía sau là:

S1 = 2 . (10 + 2) . 9 + 2 . 10 . 2 = 256 (in2)

Diện tích toàn 🎃phần của khối hộp chữ nhật phía trước🔜 là:

S2 = 2 . (6 + 2) . 9 + 2 . 6 . 2 = 168 (in2)

Phần tiếp xúc nhau của hai khối hộp trên là một hình chữ nhật có kích thước là 2 in và♔⛦ 9 in.

Diện tích toàn phần của khối ghép là:

S = (S1 + S2) – 2 . 2 . 9 = (256 + 168) – 36 = 388 (in2) 

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