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} $.

Given:

A cylindrical pillar is $50\ cm$ in diameter and $3.5\ m$ in height. 

To do:

We have to find the cost of painting the curved surface of the pillar at the rate of $12.50$ per $m^2$.

Solution:

Diameter of the cylindrical pillar $= 50\ cm$

This implies,

Radius of the pillar $(r)=\frac{50}{2}\ cm$

$=25\ cm$

$=\frac{1}{4} \mathrm{~m}$

Height of the pillar $(h)=3.5 \mathrm{~m}$

Curved surface area $=2 \pi r h$

$=2 \times \frac{22}{7} \times \frac{1}{4} \times 3.5$

$=\frac{2 \times 22 \times 1 \times 35}{7 \times 4 \times 10}$

$=\frac{11}{2} \mathrm{~m}^{2}$

Rate of painting the surface $= Rs.\ 12.50$ per $\mathrm{m}^{2}$

Total cost of painting $= Rs.\ \frac{11}{2} \times 12.50$

$= Rs.\ 68.75$

Therefore,

The total cost of painting is $Rs.\ 68.75$

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Updated on: 10-Oct-2022

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