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 (in sq. cm) is

• A. 100 $\pi$
• B. 75 $\pi$
• C. 60 $\pi$
• D. 50 $\pi$

Answer 1

The correct option is A 100 $\pi$

Volume of sphere of radiius $10cm=8\times$ (Volume of each smaller sphere)
Let the radius of the new spheres formed be $r$.
Volume of a sphere of radius 'r' $=\frac{4}{3}\pi r^3$
Hence, $\frac{4}{3}\pi \times {10}^3=8\times \frac{4}{3}\pi \times r^3$
$ { 10 }^{ 3 } = 8 \times { r }^{ 3 } $
$=>r^3=\frac{{10}^3}{8}=\frac{{10}^3}{2^3}$
$=>r=\frac{10}{2}=5cm$
Surface area of a sphere of radius 'r' $=4\pi r^2$
Hence, surface area of each sphere $=4\pi \times 5^2=100\pi$ sq cm