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Giải bài tập 10.27 trang 109 SGK Toán 9 tập 2 - Kết nối tri thức

Cho hình lập phương ABCD.A’B’C’D’ cạnh a. Tính thể tích của hình nón có đỉnh là tâm O của hình vuông ABCD và đáy là hình tròn tiếp xúc với các cạnh của hình vuông A’B’C’D’ (H.10.38).

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

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Đề bài

Cho hình lập phương ABCD.A’B’C’D’ cạnh a. Tính thể tích của hình nón có đỉnh là tâm O của hình vuông ABCD và đáy là hình tròn tiếp xúc với các cạnh của hình vuông A’B’C’D’ (H.10.38).

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Hình nón có chiều cao \(h = a\), bán kính đáy \(R = \frac{{A'B'}}{2} = \frac{a}{2}\). + Thể tích hình nón chiều cao h, bán kính R là: \(V = \frac{1}{3}\pi {R^2}h\).

Lời giải chi tiết

Hình nón đã cho có chiều cao \(h = a\). Vì đáy hình nón là đường tròn nội tiếp hình vuông A’B’C’D’ nên bán kính đáy là: \(R = \frac{{A'B'}}{2} = \frac{a}{2}\). Thể tích của hình nón là: \(V = \frac{1}{3}\pi {R^2}h = \frac{1}{3}\pi {\left( {\frac{a}{2}} \right)^2}a = \frac{{{a^3}\pi }}{{12}}\).

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