Question

The internal and external diameters of a hollow hemispherical vessel are $24$ cm and $25$ cm respectively. Find the cost of painting the vessel all over, at the rate of $5$ paise per sq.cm.

Answer 1

Internal diameter of spherical vessel $=24$ cm

External diameter of hemispherical vessel $=25$ cm

Internal radius $=r=12$ cm and External radius $=R=12.5$ cm

Total surface area to be painted

$=$ External curved surface $+$ Internal curved surface $+$ Area of ring

$=2\pi R^2+2\pi r^2+\pi (R^2-r^2)$

$=\pi (2R^2+2r^2+R^2-r^2)$

$=\pi (3R^2+r^2)$

$=\frac{22}{7}(3\times {12.5}^2+{12}^2)$

$=\frac{22}{7}(468.75+144)$

$=\frac{22}{7}\times 612.75$

$=1925.78$sq.cm

Rate of painting $=5$paise per sq.cm

Thus, cost of painting$=Area\times Rate=\frac{1925.78\times 5}{100}=$Rs.$96.29$