Question.
A cylindrical pillar is $50 \mathrm{~cm}$ in diameter and $3.5 \mathrm{~m}$ in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. $12.50$ per $\mathrm{m}^{2} .\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$
Solution:
Height $(h)$ cylindrical pillar $=3.5 \mathrm{~m}$
Radius $(r)$ of the circular end of pillar $=\frac{50}{2}=25 \mathrm{~cm}$
$=0.25 \mathrm{~m}$
CSA of pillar $=2 \pi r h$
$=\left(2 \times \frac{22}{7} \times 0.25 \times 3.5\right) \mathrm{m}^{2}$
$=(44 \times 0.125) \mathrm{m}^{2}$
$=5.5 \mathrm{~m}^{2}$
Cost of painting $1 \mathrm{~m}^{2}$ area = Rs $12.50$
Cost of painting $5.5 \mathrm{~m}^{2}$ area $=$ Rs $(5.5 \times 12.50)$
$=$ Rs $68.75$
Therefore, the cost of painting the CSA of the pillar is Rs $68.75$.
Height $(h)$ cylindrical pillar $=3.5 \mathrm{~m}$
Radius $(r)$ of the circular end of pillar $=\frac{50}{2}=25 \mathrm{~cm}$
$=0.25 \mathrm{~m}$
CSA of pillar $=2 \pi r h$
$=\left(2 \times \frac{22}{7} \times 0.25 \times 3.5\right) \mathrm{m}^{2}$
$=(44 \times 0.125) \mathrm{m}^{2}$
$=5.5 \mathrm{~m}^{2}$
Cost of painting $1 \mathrm{~m}^{2}$ area = Rs $12.50$
Cost of painting $5.5 \mathrm{~m}^{2}$ area $=$ Rs $(5.5 \times 12.50)$
$=$ Rs $68.75$
Therefore, the cost of painting the CSA of the pillar is Rs $68.75$.