The internal and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. The cost of painting 1 cm2 of the surface is 10 paise. Find the total cost to paint the vessel all over.
We are given the following hemi hollow sphere
The internal and external radii of the hollow hemispherical vessel are $\frac{21}{2}=10.5 \mathrm{~cm}$ and $\frac{25.2}{2}=12.6 \mathrm{~cm}$ respectively. Therefore, the total surface area of the hollow hemispherical vessel is
$S=2 \pi \times(12.6)^{2}+2 \pi \times(10.5)^{2}+\pi\left\{(12.6)^{2}-(10.5)^{2}\right\}$
$=2 \times \frac{22}{7} \times 158.76+2 \times \frac{22}{7} \times 110.25+\frac{22}{7} \times 48.51$
$=997.92+693+152.46$
$=1843.38$
The cost of painting 1 square cm is 10 paise. Therefore the total cost of painting the vessel all over is
$1843.38 \times 10=1843.38 \times 10$ Paise
$=184.338$ Rupees
Hence total cost of painting is $184.338$ rupees