Question

by melting a solid sphere of radius 9cm, a sphere of radius 6cm and a cylinder of same radius is formed. what is the height of the cylinder​

Answer 1

Answer:

The height of the cylinder is 19 cm.

Step-by-step-explanation:

We have given that,

A metal sphere is melted and a small sphere and a cylinder are formed.

Radius of larger sphere ( R ) = 9 cm

Radius of smaller sphere ( r ) = 6 cm

Radius of smaller sphere ( r ) = 6 cm

We have to find the height of the cylinder.

Now,

Volume of larger sphere = Volume of smaller sphere + Volume of cylinder

$\displaystyle{\implies\pink{\sf\:\dfrac{4}{3}\:\pi\:R^3\:=\:\dfrac{4}{3}\:\pi\:r^3\:+\:\pi\:r^2\:h}}$

$\displaystyle{\implies\sf\:\dfrac{4}{3}\:\times\:\cancel{\pi}\:\times\:(\:9\:)^3\:=\:\cancel{\pi}\:r^2\:\left(\:\dfrac{4}{3}\:\times\:r\:+\:h\:\right)}$

$\displaystyle{\implies\sf\:\dfrac{4}{\cancel{3}}\:\times\:\cancel{9}\:\times\:9\:\times\:9\:=\:(\:6\:)^2\:\left(\:\dfrac{4}{\cancel{3}}\:\times\:\cancel{6}\:+\:h\:\right)}$

$\displaystyle{\implies\sf\:4\:\times\:3\:\times\:9\:\times\:9\:=\:6\:\times\:6\:\times\:(\:8\:+\:h\:)}$

$\displaystyle{\implies\sf\:h\:+\:8\:=\:\dfrac{4\:\times\:\cancel{3}\:\times\:9\:\times\:\cancel{9}}{\cancel{6}\:\times\:\cancel{6}}}$

$\displaystyle{\implies\sf\:h\:+\:8\:=\:\dfrac{\cancel{4}\:\times\:9\:\times\:3}{\cancel{2}\:\times\:\cancel{2}}}$

$\displaystyle{\implies\sf\:h\:+\:8\:=\:9\:\times\:3}$

$\displaystyle{\implies\sf\:h\:+\:8\:=\:27}$

$\displaystyle{\implies\sf\:h\:=\:27\:-\:8}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:h\:=\:19\:cm\:}}}}$

∴ The height of the cylinder is 19 cm.