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# cone

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A circular sheet of paper of radius 6 inches is cut into 4 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone?

Dec 2, 2020

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A circular sheet of paper of radius 6 inches is cut into 4 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone?

Hello Guest!

$$C_{cone}=\frac{2\cdot \pi \cdot 6in}{4}=\pi \cdot 3in$$

$$r_{cone}=\frac{C_{cone}}{2\cdot \pi}=\frac{\pi \cdot 3in}{2\cdot \pi}\\ r_{cone}=\frac{3}{2}in$$

$$h_{cone}=\sqrt{(6in)^2-(r_{cone})^2}=\sqrt{36in^2-(\frac{3}{2})^2in^2}$$

$$h_{cone}=5.809\ inches$$

The height of the cone in inches is 5.809 inches.

!

Dec 3, 2020