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Giải bài tập 9.12 trang 83 SGK Toán 9 tập 2 - Cùng khám phá

Tính khối lượng thép cần dùng để sản xuất 1000 chiếc đinh tán có thân hình trụ và đầu là nửa hình cầu với kích thước như Hình 9.47, biết khối lượng riêng của thép là 7850 kg/m3.

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

Toán - Văn - Anh
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Đề bài

Tính khối lượng thép cần dùng để sản xuất 1000 chiếc đinh tán có thân hình trụ và đầu là nửa hình cầu với kích thước như Hình 9.47, biết khối lượng riêng của thép là 7850 kg/m3.

 

Phương pháp giải - Xem chi tiết

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

ꦓThể tích của hình cầu là: \(V = \frac{4}{3}\pi {R^3}\)(với R là bán kính hình cầu)

Khối lượng thép: m = V.D (D là khối lượng riêng)

Lời giải chi tiết

Thể tích phần hình trụ là:

\(V = \pi {R^2}h = \pi {.2^2}.25 = 100\pi \)(mm3)

Thể tích nửa hình cầu là:

\(V = \frac{1}{2}.\frac{4}{3}\pi {R^3} = \frac{1}{2}.\frac{4}{3}\pi {5^3} = \frac{{250}}{3}\pi \)(mm3)

Thể tích một chiếc đinh tán là:

\(100\pi + \frac{{250}}{3}\pi \approx 576\)(mm3)

Thể tích 1000 chiếc đinh tán là:

576.1000 = 576 000 (mm3) = 0,000576 (m3)

Suy ra khối lượng thép là: m = D.V = 7850.0,000576 \( \approx \) 4,5kg.

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