Mensuration-52

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A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 108 cm,and the diameter
of the hemispherical ends is 36 cm, find the cost of polishing the surface at the rate of 7 cents per square cm.

Solution: Radius of the cylinder = Radius of the two hemispheres = 36/2 cm = 18 cm

Length of the cylinder = (108 - 18 - 18) cm = 72 cm

Surface area of the cylinder = 2 Π r h

Total surface area of the two equal hemispheres = 4 Π r2

Surface area of the whole solid

= 2 Π r h + 4 Π r2

= 2 Π r (h + 2r)

= 2 x 3.1416 x 18 (72 + 2 x 18)

= 12214.54 cm2 (approx)

Therefore, cost of polishing = $ (7/100 x 12214.54) = $855.02

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