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Giải bài tập 9.17 trang 85 SGK Toán 9 tập 2 - Cùng khám phá

Người ta xếp 6 lon nước ngọt vừa khít trong một thùng carton có dạng hình hộp chữ nhật như Hình 9.51. Mỗi lon nước ngọt có thể xem là một hình trụ với đường kính 6,4 cm và cao 12 cm. a) Tính tổng thể tích của 6 lon nước ngọt. b) Các lon nước ngọt chiếm khoảng bao nhiêu phần trăm không gian trong thùng (làm tròn kết quả đến hàng phần mười)?

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Người ta xếp 6 lon nước ngọt vừa khít trong một thùng carton có dạng hình hộp chữ nhật như Hình 9.51. Mỗi lon nước ngọt có thể xem là một hình trụ với đường kính 6,4 cm và cao 12 cm. a) Tính tổng thể tích của 6 lon nước ngọt. b) Các lon nước ngọt chiếm khoảng bao nhiêu phần trăm không gian trong thùng (làm tròn kết quả đến hàng phần mười)?

Phương pháp giải - Xem chi tiết

🍌Thể tích hình trụ là: \(V = \pi {r^2}h\) (với r là bán kính đáy và h là chiều cao của hình trụ).

♏Thể tích hình hộp chữ nhật là: \(V = abh\) (với a, b là chiều dài và chiều rộng đáy và h là chiều cao của hình nón).

Lời giải chi tiết

a) Tổng thể tích của 6 lon nước ngọt là:

\(6.V = 6\pi {r^2}h = 6\pi .{\left( {3,2} \right)^2}.12 = 2316,2\) (cm3)

b) Chiều dài hình hộp chữ nhật là: 6,4.3 = 19,2 (cm) Chiều rộng hình hộp chữ nhật là: 6,4.2 = 12,8 (cm) Thể tích hình hộp chữ nhật là:

19,2.12,8. 12 = 2949, 1 (cm3)

Các lon nước ngọt chiếm \(\frac{{2316,2}}{{2949,1}}.100\%  = 78,5\% \) không gian trong thùng.

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