A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.

#### Solution

A cone has been reshaped in the sphere

Height of cone is 24 cm and the radius of the base is 6 cm

Volume of sphere = volume of cone

Volume of cone = `1/3`πr^{2}h

Plugging the values in the formula we get

volume of cone = `1/3`π(6)^{2}24 = 288π cm^{3}

Let the radius of sphere be r

Volume of sphere = `4/3`πr^{3}

Since, the volume of cone = volume of sphere

Volume of sphere = 288π cm^{3}

So,

288π = `4/3` πr^{3}

⇒ 288 = `4/3`r^{3}

⇒ r^{3 }= 216

⇒ r = 6 cm

Hence, radius of reshaped sphere is 6 cm

Now, surface area of sphere = 4πr^{2}

= 4π(6)^{2}

= `144 × 22/7`

= 452.5 cm^{2}

Therefore, surface area of sphere is 452.57 cm^{2}