Question

The internal and external diameters of a hollow hemispherical vessel is $20cm$ and $28cm$ respectively. Find the cost of painting the vessel all over at $14$ paise per ${cm}^2$.

Answer 1

External radius $=\frac{28}{2}cm=14cm$

The external surface area of vessel $=2\pi R^2$

$=2\times \frac{22}{7}\times 14\times 14$

$=1232c{m}^2....\left(1\right)$

Internal radius $=\frac{20}{2}cm=10cm$

The Internal surface area of vessel $=2\pi r^2$

$=2\times \frac{22}{7}\times 10\times 10$

$=628.57c{m}^2.....\left(2\right)$

The surface area of ring $=\pi (R^2-r^2)$

$=\frac{22}{7}({14}^2-{10}^2)$

$=301.714c{m}^2......\left(3\right)$

Total surface area of vessel $=\left(1\right)+\left(2\right)+\left(3\right)$

$=1232+628.57+301.714$

$=2162.284c{m}^2$

Cost of painting vessel $=14p/c{m}^2$

Total cost of painting $=14\times 2162.284$

$=30,271.976$ paise

We know that $1$ Rupee $=100$ paise

Hence, total cost $=Rs\frac{30271.976}{100}$

Total cost $=Rs302.72$