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Prove that for a cone made by rolling up a semicircle, the area of the curved surface is twice the base area. |
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Answer» Perimeter of base of a cone is equal to half of perimeter of large cone. Radius of pyramid = R/2 Perimeter of base \(=\pi(\frac{R}{2})^2=\pi\frac{R^2}{4}\) \(=\frac{1}{2}\pi \,R^2=\frac{\pi\,R^2}{2}=2\times\frac{\pi\,R^2}{4}\) = 2 × Base area , that is twice |
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