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Question
A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2 .
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Solution
Height of the cylinder = height of entire solid - height of sphere 1 - height of sphere 2
= 108 - 18 - 18
= 108 − 36
= 72 cm
r = 18 cm
C.S.A. of cylinder
\[= 2\pi r h\]
\[ = 2\pi \times 18 \times 72\]
\[ = 8138 . 88 {cm}^2\]
C.S.A. of 2 hemispheres = surface area of a sphere
\[= 4 \pi r^2 \]
\[ = 4\pi \left( 18 \right)^2 \]
\[ = 4069 . 44 {cm}^2\]
Surface area of solid
= 8138.88 + 4069.44
= 12208.32 cm2
Cost of polishing 1 cm2 = 7 paise = 0.07 Rs
Total cost
\[= 12208 . 32 \times 0 . 07\]
\[ = \text { Rs } 854 . 58\]
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