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Question
A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 98 cm and the diameter of each of its hemispherical ends is 28 cm, find the cost of polishing the surface of the solid at the rate of 15 paise per sq cm.
Solution
The arrangement is shown in the figure:
Diameter of the cylinder = 28 cm
Therefore ,radius of the cylinder = Radius of the hemispheres = 14 cm
Surface area of two hemispheres =`2xx2pir^ = 2xx2xx22/7xx14xx14 = 2464 "cm"^2`
`"length of cylinder"= 98 -14 xx 2 = 98 - 28 = 70`
`"Curved surface area of cylinder" = 2pirl= 2xx22/7xx14xx70 = 6160 cm^2`
`"Total surface area" = 2464 + 6160 = 8624 "cm"^2`
cost of polishing the entire object = 8624 × 15 = 129360 paise = Rs 1293.60.
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