Question

Eight spheres of same radius from a metallic sphere of $10cm$ radius, are formed. Find the surface area of each sphere so obtained.

Answer 1

Volume of sum of all small spheres=Volume of big sphere

Volume of one small sphere$=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (10{)}^3=1000\frac{4\pi }{3}$

Volume of all 8 small spheres$=8\times 1000\times \frac{4\pi }{3}$ (1)

Let radius of big sphere be R

Volume of big sphere$=\frac{4}{3}\pi R^3$ (2)

Equating (1) and (2)

$8\times 1000\times \frac{4\pi }{3}=\frac{4}{3}\pi R^3$

$8000=R^3$

$R=20cm$

Surface Area of sphere$=4\pi R^2=4\pi \times 10\times 10=4\times 314=1256c{m}^3$

Hence surface area of sphere$=1256c{m}^3$