Question

Outer surface area of a hollow iron sphere is $1256c{m}^2$. If the thickness of iron is $1cm$, find the volume of air inside the sphere. Take $\pi =3.14$

• A. $3052.08c{m}^3$​
• B. $3051.08c{m}^3$​
• C. $3053.08c{m}^3$​
• D. $3054.08c{m}^3$​

Answer 1

The correct option is A

$3052.08c{m}^3$​

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 = 1cm
So, inner radius = 9 cm

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