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# geometry

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A cone is formed by rotating an isosceles right triangle with leg length 10 about one of its legs. Its surface area is pi times what number?

Oct 1, 2020

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A cone is formed by rotating an isosceles right triangle with leg length 10 about one of its legs. Its surface area is pi times what number?

Hello Guest!

$$A=A_{\circ}+A_M$$

$$A_{\circ}=10^2\cdot \pi$$

$$A_M=\pi\cdot r\cdot s=\pi\cdot 10\cdot 10\sqrt{2}\\ A_M=\pi\cdot 10^2\cdot \sqrt{2}$$

$$\color{black}A=\pi \cdot(10^2+10^2\cdot \sqrt{2})\\ A=\pi\cdot 10^2(1+\sqrt{2})\\ A=\pi \cdot 241.421$$

The surface area is $$\pi \cdot 241.421$$

!.

Oct 2, 2020
edited by asinus  Oct 2, 2020