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. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Volume of cone $=\frac{1}{3}\times \pi \times r^2\times h=\frac{1}{3}\times \pi \times 6\times 6\times 24c{m}^3$

If r is the radius of the sphere, then its volume is $\frac{4}{3}\pi r^3$ .

Since, the volume of clay in the form of the cone and the sphere remains the same, we have

$\frac{4}{3}\times \pi \times r^3=\frac{1}{3}\times \pi \times 6\times 6\times 24$

i.e., $r^3=3\times 3\times 24=3^3\times 2^3$

So $r=3\times 2=6$

Therefore, the radius of the sphere is 6 cm.