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Lý thuyết Hình cầu Toán 9 Kết nối tri thức

Đặc điểm hình cầu Một số yếu tố của hình cầu: Tâm mặt cầu: O. Bán kính mặt cầu: \(R = OB\).

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

Toán - Văn - Anh
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Đặc điểm hình cầu

Một số yếu tố của hình cầu: Tâm mặt cầu: O. Bán kính mặt cầu: \(R = OB\).

Phần chung giữa mặt phẳng và mặt cầu

1. Nếu cắt một hình cầu bởi một mặt phẳng thì phần chung của mặt phẳng và hình cầu (còn gọi là mặt cắt) là một hình tròn. 2. Nếu cắt một mặt cầu bán kính R bởi một mặt phẳng thì phần chung của mặt phẳng và mặt cầu là một đường tròn.

• Khi mặt phẳng đi qua tâm thì đường tròn đó có bán kính R và được gọi là đường tròn lớn. • Khi mặt phẳng không đi qua tâm thì đường tròn đó có bán kính nhỏ hơn R.

Diện tích mặt cầu

Công thức tính diện tích mặt cầu: \(S = 4\pi {R^2}\), trong đó R là bán kính.

Thể tích hình cầu

Công thức tính thể tích hình cầu: \(V = \frac{4}{3}\pi {R^3}\), trong đó R là bán kính.

Ví dụ:

Diện tích mặt cầu là:\(S = 4\pi {R^2} = 4\pi {.10^2} = 400\pi \left( {c{m^2}} \right)\),Thể tích hình cầu là:\(V = \frac{4}{3}\pi {R^3} = \frac{4}{3}\pi {.10^3} = \frac{{4000\pi }}{3}\left( {c{m^3}} \right)\).

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