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 $100c{m}^2$.

Answer 1

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
$=2\pi rh+2\times 2\pi r^2=2\pi r(h+2r)$
$=2\times \frac{22}{7}\times 7[90+2(7\left)\right]c{m}^2$
$=44\times 104c{m}^2=4576c{m}^2$
$\therefore$ TSA of the solid$=4.576c{m}^2$
Cost of polishing at the rate of Rs.$4$ per $100c{m}^2$
$=4576\times \frac{Rs.4}{100}=Rs.183.04$
$\therefore$ Cost of polishing the solid$=Rs.183.04$.