A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed.

Given:

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made.

To do:

We have to find the number of such cones formed. 

Solution:

Radius of the solid metallic sphere $R=5.6 \mathrm{~cm}$

This implies,

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

$=\frac{4}{3} \pi \times(5.6)^{3}$

$=\frac{702.464}{3} \pi \mathrm{cm}^{3}$

Radius of each cone $r=2.8 \mathrm{~cm}$

Height of each cone $h=3.2 \mathrm{~cm}$

This implies,

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

$=\frac{1}{3} \pi(2.8)^{2} \times 3.2$

$=\frac{25.088}{3} \pi \mathrm{cm}^{3}$

Therefore,

Number of cones formed $=\frac{\text { Volume of the sphere }}{\text { Volume of each cone }}$

$=\frac{702.464 \pi \times 3}{3 \times 25.088 \pi}$

$=28$

The number of such cones formed is $28$.

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Updated on: 10-Oct-2022

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