Question

Twenty one 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?

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{Diameter}\mathrm{of}\mathrm{the}\mathrm{pillars}=0.5\mathrm{m} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{pillars},r=0.25\mathrm{m} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{pillars},h=4\mathrm{m} \\ \mathrm{Number}\mathrm{of}\mathrm{pillars}=21 \\ \mathrm{Rate}\mathrm{of}\mathrm{cleaning}=\mathrm{Rs}2.50\mathrm{per}\mathrm{square}\mathrm{metre} \\ \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{one}\mathrm{pillar}=2\mathrm{\pi }rh \\ =2\times \frac{22}{7}\times 0.25\times 4 \\ =2\times \frac{22}{7} \\ =\frac{44}{7}{\mathrm{m}}^2 \\ \therefore \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{one}\mathrm{pillar}=\frac{44}{7}{\mathrm{m}}^2 \\ \mathrm{Cost}\mathrm{of}\mathrm{cleaning}21\mathrm{pillars}\mathrm{at}\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{Rs}2.50\mathrm{per}{\mathrm{m}}^2=\mathrm{Rs}2.5\times 21\times \frac{44}{7} \\ =7.5\times 44 \\ \therefore \mathrm{Cost}\mathrm{of}\mathrm{cleaning}21\mathrm{pillars}\mathrm{at}\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{Rs}2.50\mathrm{per}{\mathrm{m}}^2=\mathrm{Rs}330 \end{gathered}$$