Question

The hemispherical dome of a building needs to be painted. If the circumference of the base of dome is $17.6$, find the cost of painting it, given the cost of painting is $Rs.5$ per $100c{m}^2$.

Answer 1

Since only the rounded surface of the dome is to be painted we need to find the curved surface area of the hemisphere to know the extent of painting that needs to be done.
Now, circumference of base of the dome = 17.6 m Therefore 17.6 = 2$\pi$r
So, The radius of the dome $=17.6\times \frac{7}{2\times 22}m$

= 2.8 m
The curved surface area of the dome $=2\pi r^2$

$=2\times \frac{22}{7}\times 2.8\times 2.8m^2$
$=49.28m^2$

Now, cost of painting 100 cm${}^2$ is Rs. 5
So, cost of painting 1 m${}^2$ = Rs. 500
Therefore, cost of painting the whole dome
$=Rs.500\times 49.28$

$=Rs.24640$