Mensuration-54

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The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint
1 cm2 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 R2 - Π r2

Therefore, Total area to be painted = (2 Π R2 + 2 Π r2 + Π R2 - Π r2)

= Π (3 R2 + r2)

= 22/7 x [3 x (12.5)2 + 122] cm2 = 22/7 x [3 x 125/10 x 125/10 + 144] cm2

= 22/7 x (1875/4 + 144) cm2 = 22/7 x (1875 + 576)/4 cm2 = 11/7 x 2451/2 cm2

= 26961/14 cm2 = 1925.79 cm2

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

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