Question

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls off 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

$100\pi$

Radius of a sphere $\left(r\right)=10cm$

$\therefore Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (10{)}^{3}c{m}^3$

$=\frac{4000}{3}\pi c{m}^3$

Then volume of 8 balls $=\frac{400}{3}\pi c{m}^3$

$\therefore Volumeof1ball=\frac{4000}{8\times 3}\pi =\frac{500}{3}\pi c{m}^3$

$Thenradius=3\sqrt{\frac{Volume}{\frac{4}{3}\pi }}$

$=3\sqrt{\frac{500\pi \times 3}{3\times 4\pi }}=3\sqrt{125}$

$=3\sqrt{5^3}=5cm$

Now surface area of each ball

$=4\pi r^2=4\times \pi \times 5^2$

$=4\times \pi \times 5\times 5=100\pi c{m}^3$