Question

The internal and external diameter of a hollow hemi-spherical vessel is $24cm$ and $25cm$ respectively. The cost of paint one sq.cm of the surface is paise. Find the total cost to paint the vessel all over.

Answer 1

As surface area of hemisphere with radius $r=2\pi r_1^2$

$\Rightarrow$ Total surface area would be $=2\pi r_1^2+2\pi r_2^2$

$=2\pi ({\left(\frac{24}{2}\right)}^2+{\left(\frac{25}{2}\right)}^2)$

$=\frac{2\pi }{4}(576+625)=\frac{\pi }{2}\left(1201\right)c{m}^2$

As cost of painting per sq. cm is $1$ paise

$\Rightarrow$ Total cost$=\frac{1201\pi }{2}$ paise

$=1885.57$ paise.