Question

How many cubic metres of earth must be dug out to make a well $28$ m deep and $2.8$ m in diameter? Also, find the cost of plastering its inner surface at Rs.$4.50$ per sq.m.

• A. $142.48m^3$ ; Rs. $1108.80$
• B. $153.48m^3$ ; Rs. $1008.80$
• C. $172.48m^3$ ; Rs. $1108.80$
• D. $112.48m^3$ ; Rs. $1008.80$

Answer 1

The correct option is C $172.48m^3$ ; Rs. $1108.80$

Given, Earth has to dug out to make well $2.8m$ in diameter and $28m$ in height.

Also cost of plastering the inner wall is $4.50persq.m$
Radius $=\frac{\text{Diameter}}{2}=1.4m$
Well is cylindrical in shape.
So,

Volume of well to be dug out $=\pi r^{2}h$

$\Rightarrow V=\frac{22}{7}\times {1.4}^2\times 28$

$\Rightarrow V=172.48m^3$

To find cost of plastering of we have to first find curved surface area of inner wall.
Curved surface area $=2\pi rh$

$\Rightarrow CSA=2\times \frac{22}{7}\times 1.4\times 28$

$\Rightarrow CSA=246.4m^2$

Cost of plastering $=$ Curved Surface Area$\times$ Rate per sq. meter

Cost $=246.4\times Rs.4.50$

$\Rightarrow$ Cost $=Rs.1108.8$

Hence, option C.