(i) How many cubic meters of soil must be dug out to make a well 20 meters deep and 2 meters in diameter ?

(ii) If the inner curved surface of the well in part (i) above is to be plastered at the rate of ₹ 50 per m², find the cost of plastering.

(i) A well needs to be formed which is 20 meters deep and has a diameter of 2 meters.

Height of well = 20 m

Radius = $\dfrac{\text{Diameter}}{2} = \dfrac{2}{2}$ = 1 m.

Volume of soil to be dug out = Volume of well to be formed.

Volume of cylinder = πr²h.

Putting values we get,

$\text{Volume of well } = \dfrac{22}{7} \times (1)^2 \times 20 \\[1em] = \dfrac{22 \times 1 \times 20}{7} \\[1em] = \dfrac{440}{7} \\[1em] = 62\dfrac{6}{7} \text{ m}^3.$

Hence, $62\dfrac{6}{7} \text{ m}^3$ of soil must be dug out for the formation of well.

(ii) Curved surface area of cylinder = 2πrh

= $2 \times \dfrac{22}{7} \times 1 \times 20 = \dfrac{880}{7} \text{m}^2.$

Rate of plastering = ₹ 50/m².

So, plastering well will cost = $\dfrac{880}{7} \times 50 = \dfrac{44000}{7}$ = ₹ 6285.70

Hence, the cost of plastering the inner curved surface area of the well = ₹ 6285.70.