Question

Outer surface area of a hollow iron sphere is 1256 cm${}^2$. If thickness of iron is 1 cm, its capacity = .

• A. 3052.08 $c{m}^3$
• B. 3051.08 $c{m}^3$
• C. 3053.08 $c{m}^3$

Answer 1

The correct option is A 3052.08 $c{m}^3$

Surface area of the sphere
= $4\pi$ $r^2=1256m^2$
$\Rightarrow 4$ $\times$ $3.14\times$ $r^2=1256c{m}^2$
$\Rightarrow r=10cm$
Thickness of the iron = 1 cm
So, inner radius = 9 cm

Therefore,
volume of air
= inner volume of sphere
$=\frac{4}{3}$ $\times$$\pi$ $\times$ $r^3$
$=\frac{4}{3}$ $\times$ $3.14$ $\times$ $9^3$
$=3052.08c{m}^3$​