Question

The cost of painting the surface of a sphere is Rs. $1526$ at the rate of Rs. $6$ per ${\text{m}}^2$. Find the radius of the sphere. $(\pi =3.14)$

Answer 1

$\text{Rs.}1526$ is spent to a paint a sphere at the rate of $\text{Rs.}6/m^2$.

Area of region painted at the cost of $\text{Rs.}6=1{\text{m}}^2$

Area of the region painted for $\text{Rs.}1526=\frac{1526}{6}=\frac{763}{3}{m}^2$
Surface area of the sphere $=4\pi r^2$
$\Rightarrow \frac{763}{3}=4\times 3.14\times r^2$
$\Rightarrow r^2=\frac{763}{3}\times \frac{1}{4\times 3.14}$
$\Rightarrow r^2=20.25$
$\Rightarrow r=4.5\text{cm}$