Question

A cylinder has hemispherical ends having radius 7 cm and total height of solid is 104 cm. If its outer surface is to polished & cost of polish is Rs. 100 per sq. mtr. find the total cost of polish.

Answer 1

Radius of each hemisphere = r = 7 cm
Height of total solid = 104 c
Height of cylinder, $h=104-2\times 7=90cm$
Then,
T.S.A. of the solid = C.S.A. of the cylinder + 2 $\times$ C.S.A. of the hemisphere
$=2\pi rh+2\times 2\pi r^2$
$=2\pi r(h+2r)$
$=2\times \frac{22}{7}\times 7(90+2\times 7)$
$=44\times 104$
$=4576c{m}^2$
$=0.4576m^2$
$\therefore$ Total surface of the given solid is 0.4576 m${}^2$.
Cost of polish is Rs. 100 per sq. mtr.
$\therefore$ Cost of polishing the solid of area $0.4576m^2=0.4576\times 100=45.76$
Total cost of polish is Rs. 45.76.