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Question

A solid is composed of a cylinder with hemispherical ends. If the whole lengthe of the solid is $$104$$cm and the radius of each hemispherical end is $$7$$cm, find the cost of polishing its surface at the rate of Rs. $$4$$ per $$100cm^2$$.


Solution

Hemispherical part: $$r=7cm$$
Cylindrical part: $$r=7cm, h=104-(7+7)=90cm$$
Total surface area of the solid$$=$$ CSA of cylindricall part$$+2\times $$CSA of hemispherical part
$$=2\pi rh+2\times 2\pi r^2=2\pi r(h+2r)$$
$$=2\times \displaystyle\frac{22}{7}\times 7[90+2(7)]cm^2$$
$$=44\times 104cm^2=4576cm^2$$
$$\therefore$$ TSA of the solid$$=4.576cm^2$$
Cost of polishing at the rate of Rs.$$4$$ per $$100cm^2$$
$$=4576\times\displaystyle\frac{Rs.4}{100}=Rs.183.04$$
$$\therefore$$ Cost of polishing the solid$$=Rs. 183.04$$.
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Mathematics

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