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. (Use π = 3.1416)
Solution:
Height of the cylinder
$=108-36$
$=72 \mathrm{~cm}$
$r=18 \mathrm{~cm}$
C.S.A. of cylinder
$=2 \pi r h$
$=2 \pi \times 18 \times 72$
$=2 \times 3.14 \times 18 \times 72$
$=8138.88 \mathrm{~cm}^{2}$
C.S.A. of 2 hemisphere = surface of a sphere
$=4 \pi r^{2}$
Total surface
$=2 \pi r h+4 \pi r^{2}$
$=2 \pi r(h+2 r)$
$=2 \times 3.14 \times 18(72+2 \times 18)$
$=12214.54 \mathrm{~cm}^{2}$
Total cost
$=7 \times 12214.54$
$=85502$ Paise
$=855.02$ Rs.