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

Answer: (D)

100π cm2

Answer 2

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