A metallic sphere of radius $10.5\ cm$ is melted and thus recast into small cones each of radius $3.5\ cm$ and height $3\ cm$. Find how many cones are obtained.

 Given:

A metallic sphere of radius $10.5\ cm$ is melted and thus recast into small cones each of radius $3.5\ cm$ and height $3\ cm$.

To do:

We have to find the number of cones obtained.

Solution:

Radius of the metallic sphere $(R) = 10.5\ cm$

This implies,

Volume of the sphere $=\frac{4}{3} \pi R^{3}$

$=\frac{4}{3} \pi(10.5)^{3}$

$=\frac{4}{3} \pi \times 1157.625 \mathrm{~cm}^{3}$

Radius of a small cone $=3.5 \mathrm{~cm}$

Height of a cone $=3 \mathrm{~cm}$

Therefore,

Volume of each cone $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \pi(3.5)^{2} \times 3$

$=\frac{1}{3} \pi 12.25 \times 3$

$=12.25 \pi \mathrm{cm}^{3}$

Number of cones made from the sphere $=\frac{4 \times 1157.625 \pi}{3 \times 12.25 \pi}$

$=126$

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Updated on: 10-Oct-2022

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