Question

# a right circular cone is 4.1 cm high and the radius of its base is 2.1 cm another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm both the cones are melted together and recast into a sphere. find the diameter of the sphere.

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Solution

## $Volumeofthefirstcone=\frac{\pi ×2.{1}^{2}×4.1}{3}\phantom{\rule{0ex}{0ex}}Volumeofthesecondcone=\frac{\pi ×2.{1}^{2}×4.3}{3}\phantom{\rule{0ex}{0ex}}totalmaterial=\frac{\pi ×2.{1}^{2}}{3}\left(4.1+4.3\right)=12.348\pi c{m}^{3}\phantom{\rule{0ex}{0ex}}iftheradiusofthesphere=r\phantom{\rule{0ex}{0ex}}then\frac{4\pi {r}^{3}}{3}=12.348\pi \phantom{\rule{0ex}{0ex}}r=2.08cm\phantom{\rule{0ex}{0ex}}diameterofthesphere=4.16cm\phantom{\rule{0ex}{0ex}}$

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