Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is $0.50\ m$ and height is $4\ m$. What will be the cost of cleaning them at the rate of $Rs.\ 2.50$ per square metre?
Given:
Twenty cylindrical pillars of the Parliament House are to be cleaned.
The diameter of each pillar is $0.50\ m$ and height is $4\ m$.
To do:
We have to find the cost of cleaning the pillars at the rate of $Rs.\ 2.50$ per square metre.
Solution:
Number of pillars $= 20$
Diameter of each pillar $= 0.50\ m$
This implies,
Radius $(r)=\frac{0.50}{2}$
$=0.25 \mathrm{~m}$
$=25 \mathrm{~cm}$
Height of each pillar $=4 \mathrm{~m}$
Therefore,
Curved surface area of each pillar $=2 \pi r h$
$=2 \times \frac{22}{7} \times \frac{25}{100} \times 4$
$=\frac{44}{7} \mathrm{~m}^{2}$
Total area of 20 pillars $=20\times\frac{44}{7}$
$=\frac{880}{7} \mathrm{~m}^{2}$
Rate of cleaning the pillars $=Rs.\ 2.50$ per $\mathrm{m}^{2}$
Total cost of cleaning $=Rs.\ 2.50 \times \frac{880}{7}$
$=Rs.\ \frac{250 \times 880}{100 \times 7}$
$=Rs.\ \frac{2200}{7}$
$=Rs.\ 7314.28$
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