Question

Earth is dugout to make a well $28m$ deep and $2.8m$ in diameter. Find the cost of plastering its inner surface at $Rs.4.50$ per sq. metre.

• A. $Rs.1136.52$
• B. $Rs.1209.24$
• C. $Rs.1010.86$
• D. None of the above

Answer 1

The correct option is A $Rs.1136.52$

The well dug is in the shape of a cylinder.

Radius of the well $=\frac{2.8}{2}=1.4m$

Volume of a Cylinder of Radius "R" and height "h" $=\pi R^{2}h$
Hence, amount of earth dug $=\frac{22}{7}\times 1.4\times 1.4\times 28=172.48m^3$

To plaster the surface, we need to plaster the side walls and the base.

Total Surface Area of a Cylinder of Radius "R" and height "h" $=2\pi R(R+h)$
Hence, TSA of the wall $=2\times \frac{22}{7}\times 1.4(1.4+28)=258.72sqm$

We need to subtract the surface of the top open end from this calculated as we need to plaster the inner surface only,

which is $\pi r^2=\frac{22}{7}\times 1.4\times 1.4=6.16m^2$

So, the area to be plastered $=258.72-6.16=252.56m^2$

Cost of plastering its inner surface at Rs $4.5$ per sq. metre $=196.56\times 4.5=Rs.1136.52$