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Mathematics

(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.

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Answer

(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 = Diameter2=22\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,

Volume of well =227×(1)2×20=22×1×207=4407=6267 m3.\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, 6267 m362\dfrac{6}{7} \text{ m}^3 of soil must be dug out for the formation of well.

(ii) Curved surface area of cylinder = 2πrh

= 2×227×1×20=8807m2.2 \times \dfrac{22}{7} \times 1 \times 20 = \dfrac{880}{7} \text{m}^2.

Rate of plastering = ₹ 50/m2.

So, plastering well will cost = 8807×50=440007\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.

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