# Mensuration-54

### From Homeworkwiki

**The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint**

**1 cm ^{2} of the surface is $ 0.10. Find the total cost to paint the vessel all over.**

**Solution:** Let the external and internal radii of the hemispherical vessel be R cm and r cm respectively. Then, R = 12.5 cm and r = 12 cm

Now, area of the outer surface = 2 Π R^{2} - Π r^{2}

Therefore, Total area to be painted = (2 Π R^{2} + 2 Π r^{2} + Π R^{2} - Π r^{2})

= Π (3 R^{2} + r^{2})

= 22/7 x [3 x (12.5)^{2} + 12^{2}] cm^{2} = 22/7 x [3 x 125/10 x 125/10 + 144] cm^{2}

= 22/7 x (1875/4 + 144) cm^{2} = 22/7 x (1875 + 576)/4 cm^{2} = 11/7 x 2451/2 cm^{2}

= 26961/14 cm^{2} = 1925.79 cm^{2}

Cost of painting = $ (1925.79 x 0.10) = $ 192.58