A solid metallic sphere of radius $ 10.5 \mathrm{~cm} $ is melted and recast into a number of smaller cones, each of radius $ 3.5 \mathrm{~cm} $ and height $ 3 \mathrm{~cm} $. Find the number of cones so formed.

Given:

A solid metallic sphere of radius \( 10.5 \mathrm{~cm} \) is melted and recast into a number of smaller cones, each of radius \( 3.5 \mathrm{~cm} \) and height \( 3 \mathrm{~cm} \).

To do:

We have to find the number of cones so formed.

Solution:

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

Radius of each cone $r=3.5\ cm$

Height of each cone $h=3\ cm$

This implies,

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

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

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

Number of cones so formed $=$ Volume of the solid metallic sphere $\div$  Volume of each cone

$=\frac{\frac{4}{3} \pi \times 10.5 \times 10.5 \times 10.5}{\frac{1}{3} \pi \times 3.5 \times 3.5 \times 3.5}$

$=126$

The number of cones formed is $126$.

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Updated on: 10-Oct-2022

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