A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Given:

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm.

To do:

We have to find the height of the cylinder. 

Solution:

Radius of the metallic sphere$r_1=4.2\ cm$.

Radius of the cylinder$r_2=6\ cm$

 Let the height of the cylinder be h.

The cylinder fromed by recasting the sphere will be same in volume.

Therefore,

Volume of sphere $=$ Volume of cylinder

$\frac{4}{3} \pi (r_1)^3= \pi (r_2)^2h$

$\frac{4}{3}\times\frac{22}{7}(4.2)^3=\frac{22}{7}\times(6)^2h$

$h=\frac{4\times4.2\times4.2\times4.2}{3\times6\times6}$

$h=1.4\times1.4\times1.4$

$h=2.74\ cm$

The height of the cylinder formed is 2.74 cm.

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Updated on: 10-Oct-2022

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