Mensuration-17

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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 sq. cm. (Take π = 3.1416)

Solution: Radius of the cylinder = Radius of the hemisphere

= 36/2 = 18 cm

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

Surface area of the cylinder = 2 π r h

= 2 x 3.1416 x 18 x 72 sq. cm

Surface area of two equal hemisphere = 2 x 2 π r2

= 4 π r2

= 4 x 3.1416 x 18 x 18 sq. cm.

Total surface area = (2 x 3.1416 x 18 x 72) + (4 x 3.1416 x 18 x 18) sq. cm

= 12214.5 sq. cm (approximately)

Cost of polishing 1 sq. cm = 7 cents

Total cost = $ 7/100 x 12214.5

= $ 855.02

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