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Giải bài 3 trang 107 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Tính diện tích của mặt cầu có thể tích là: a) 450 m3 b) 250 dm3 c) 62 cm3 (Làm tròn kết quả đến hàng đơn vị của mét vuông, đềximét vuông, xăngtimét vuông).

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

Toán - Văn - Anh
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Đề bài

Tính diện tích của mặt cầu có thể tích là:

a) 450 m3

b) 250 dm3

c) 62 cm3

(Làm tròn kết quả đến hàng đơn vị của mét vuông, đềximét vuông, xăngtimét vuông).

Phương pháp giải - Xem chi tiết

Diện tích mặt cầu là: \(S = 4\pi {R^2}\). Thể tích hình cầu là: \(V = \frac{4}{3}\pi {R^3}\).

Lời giải chi tiết

a) Ta có \(V = \frac{4}{3}\pi {R^3}\), suy ra 🌄\(R = \sqrt[3]{{\frac{{3V}}{{4\pi }}}} = \sqrt[3]{{\frac{{1350}}{{4\pi }}}}\) (m)

♛\(S = 4\pi {R^2} = 4\pi {\left( {\sqrt[3]{{\frac{{1350}}{{4\pi }}}}} \right)^2} \approx 284\) (m2)

b) Ta có \(V = \frac{4}{3}\pi {R^3}\), suy ra 🐠\(R = \sqrt[3]{{\frac{{3V}}{{4\pi }}}} = \sqrt[3]{{\frac{{750}}{{4\pi }}}}\) (m)

൩\(S = 4\pi {R^2} = 4\pi {\left( {\sqrt[3]{{\frac{{750}}{{4\pi }}}}} \right)^2} \approx 192\) (dm2)

c) Ta có \(V = \frac{4}{3}\pi {R^3}\), suy ra ไ\(R = \sqrt[3]{{\frac{{3V}}{{4\pi }}}} = \sqrt[3]{{\frac{{186}}{{4\pi }}}}\) (m)

ജ\(S = 4\pi {R^2} = 4\pi {\left( {\sqrt[3]{{\frac{{186}}{{4\pi }}}}} \right)^2} \approx 76\) (dm2)

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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