Question

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball is

• A. 60π cm²
• B. 50π cm²
• C. 75π cm²
• D. 100π cm²

Answer 1

The Correct Option is D

Assume the radius of each small spherical ball be \(r\ cm\)

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

= \(8 × \frac{4}{3} \pi (r)^3 = \frac{4}{3} \pi (10)^3\)

\(r^3 = \frac{10^3}{8}\)

\(r = \frac{10}{2}\)

\(r = 5\ cm\)

Surface area of a sphere = \(4 \pi r^2\)

= \(4 × \pi × (5)^2\) = \(100 \pi\ cm^2\)

The correct option is (D): 100π cm²