Question

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.

Answer 1

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`πr²h

Plugging the values in the formula we get
volume of cone = `1/3`π(6)²24 = 288π cm³

Let the radius of sphere be r
Volume of sphere = `4/3`πr³
Since, the volume of cone = volume of sphere
Volume of sphere = 288π cm³
So,
288π = `4/3` πr³

⇒ 288 = `4/3`r³

⇒ r³ = 216

⇒ r = 6 cm
Hence, radius of reshaped sphere is 6 cm
Now, surface area of sphere = 4πr²
 = 4π(6)²
= `144 × 22/7`
= 452.5 cm²
Therefore, surface area of sphere is 452.57 cm²