The radius of a solid sphere is 42 cm. It is melted to form identical small solid spheres whose radius is 7 cm. What is the number of small solid spheres obtained ?

Question

Question

This question was previously asked in

SSC CGL Tier 2 Quant Previous Paper (Held On: 8 Aug 2022)

Answer 1

Given:

The radius of a solid sphere(R) is 42 cm

It is melted to form identical small solid spheres whose radius(r) is 7 cm

Formula Used:

Volume of sphere= \(\frac{4}{3}\times\pi\times r^3\)

Calculations:

Let the number of spheres that can be formed be x

⇒ Volume of sphere= \(\frac{4}{3}\times\pi\times R^3=\frac{4}{3}\times\pi\times 42^3\)

It is melted into the small sphere

The volume of sphere= Volume of the small sphere

⇒ \(\frac{4}{3}\times\pi\times 42^3=x\times\frac{4}{3}\times\pi\times 7^3\)

⇒ x= 6 x 6 x 6=216

Hence, The identical small solid sphere that can be formed is 216