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Lý thuyết Hình cầu Toán 9 Chân trời sáng tạo

1. Hình cầu Định nghĩa 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 (hay mặt cầu).

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

Toán - Văn - Anh
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1. Hình cầu

Định nghĩa

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 (hay mặt cầu).

Phần chung của mặt phẳng và mặt cầu

Khi cắt hình cầu bởi một mặt phẳng thì phần chung của mặt cầu và mặt phẳng (còn gọi là mặt cắt) là một hình tròn.

2. Diện tích của mặt cầu

Diện tích S của mặt cầu có bán kính R là: \(S = 4\pi {R^2}\).

Ví dụ:

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

3. Thể tích hình cầu

Thể tích của hình cầu có bán kính R là \(V = \frac{4}{3}\pi {R^3}\).

Ví dụ:

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

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