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Giải bài tập 2 trang 97 SGK Toán 9 tập 2 - Chân trời sáng tạo

Quan sát hình cầu ở Hình 16. Hãy cho biết tâm, bán kính, diện tích mặt cầu và thể tích của hình cầu đó.

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

Toán - Văn - Anh
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Đề bài

Quan sát hình cầu ở Hình 16. Hãy cho biết tâm, bán kính, diện tích mặt cầu và thể tích của hình cầu đó.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

-  Khi quay nửa hình tròn tâm O, bán kính R một vòng quanh đường kính AB cố định ta được một hình cầu tâm O, bán kính R. Khi đó, nửa đường tròn quét thành một mặt cầu. Ta cũng gọi O và R lần lượt là tâm và bán kính của mặt cầu đó. Đoạn thẳng đi qua tâm của hình cầu với hai đầu mút nằm trên mặt cầu gọi là đường kính của hình cầu. -  Công thức thể tích của hình cầu có bán kính R là: V = \(\frac{4}{3}\pi {R^3}\). -  Diện tích mặt cầu là: S = \(4\pi {R^2}\) 

Lời giải chi tiết

Tâm của hình cầu là A. Bán kính có độ dài 6 cm.

Diện tích mặt cầu là: S = \(4\pi {R^2}\) = 144 \(\pi \)(cm2).

Thể tích của hình cầu là: V = \(\frac{4}{3}\pi {R^3} = 288\pi \) (cm3).

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