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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 its surface at the rate of 70 paise per square cm.

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857.55

855.36

366.89

758.65

answer is B.

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Detailed Solution

Given a solid made of cylinder and hemispherical ends.
Whole length is 108cm, diameter of hemispherical ends is 36cm.
Draw the required figure,
Question Image

CSA of cylinder

= 2 π r h

, here r is radius, h is height.
CSA of hemisphere

= 2 π r 2

Now,
Total surface area = curved surface of the cylinder + surface areas of hemispherical ends

⇒ (2 π r h + 2 × 2 π r 2) c m 2 ⇒ (2 π r h + 4 π r 2) c m 2 ⇒ 2 π r (h + 2 r) c m 2

Solving further,

⇒ 2 × 227 × 18 × (72 + 36) c m 2 ⇒ 12219.42 c m 2

Rate of polishing 7 paise per sq.cm
The cost of polishing is,

⇒ 12219.42 × 7100 ⇒ R s .855.36

Thus, the cost of polishing its surface at the rate of 70 paise per square cm is Rs.855.36 .
Therefore, option (2) is correct.

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