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Question

A metallic sphere of radius $$15\ cm$$ is melted and recast into the shape of a cylinder of radius $$15\ cm$$. Find the height of the cylinder.


Solution

The radius of Metallic sphere is $$15\ cm$$
The volume of sphere $$=\dfrac{4}{3}\pi r^3$$ 
                                    $$=\dfrac{4}{3}\times \pi\times 15\times 15 \times 15$$
                                    $$=4500\pi$$ $$cm^3$$


The volume of sphere is same as volume of cylinder. Let $$h$$ be the height of the cylinder.

Volume of cylinder$$=\pi\times r^2\times h$$
                              $$\pi\times 15\times 15\times h$$
                              $$225\pi h\ cm^3$$

According to the given condition,

$$225\pi h=4500\pi$$

Thus, $$h=20\ cm$$


So the height of the cylinder is $$20\ cm$$

Mathematics

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