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Bài 7.32 trang 63 SGK Toán 11 tập 2 - Kết nối tri thức

Từ một tấm tôn hình vuông có cạnh 8dm, bác Hùng cắt bỏ bốn phần như nhau ở bốn góc

🎉Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Từ một tấm tôn hình vuông có cạnh 8dm, bác Hùng cắt bỏ bốn phần như nhau ở bốn góc, sau đó bác hàn các mép lại để được một chiếc thùng (không có nắp) như Hình 7.99.

a) Giải thích vì sao chiếc thùng có dạng hình chóp cụt. b) Tính cạnh bên của thùng. c) Hỏi thùng có thể chứa được nhiều nhất bao nhiêu lít nước?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Thể tích khối chóp cụt đều \(V = \frac{1}{3}.h.\left( {S + S' + \sqrt {S.S'} } \right)\)

Lời giải chi tiết

a) AB // A’B’ \( \Rightarrow \) AB // (A’B’C’D’), AD // A’D’ \( \Rightarrow \) AD // (A’B’C’D’) Do đó (ABCD) // (A’B’C’D’). Chiếc thùng có dạng hình chóp cụt vì khi bác Hùng cắt bỏ bốn phần như nhau ở bốn góc của tấm tôn vuông, sẽ tạo thành bốn tam giác vuông cân. Vậy chiếc thùng có dạng hình chóp cụt. b) Cạnh bên của hình chóp cụt bằng \(\sqrt {\frac{9}{4} + \frac{{25}}{4}}  = \frac{{\sqrt {34} }}{2}\left( {dm} \right)\) c) Xét mặt chứa đường chéo của hình vuông, nó là hình thang cân có chiều cao bằng chiều cao của hình chóp cụt và được \(h = \sqrt {\frac{{34}}{4} - \frac{{18}}{4}}  = 2\left( {dm} \right)\) Thể tích cần tìm là V = 42 lít.

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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