Find the cost of sinking a tube-well 280 m deep, having a diameter 3 m at the rate of ₹ 15 per cubic metre.
Question:

Find the cost of sinking a tube-well 280 m deep, having a diameter 3 m at the rate of ₹ 15 per cubic metre. Find also the cost of cementing its inner curved surface at ₹ 10 per square metre.

Solution:

Height of the tube-well, h = 280 m

Radius of the tube-well, $r=\frac{3}{2} \mathrm{~m}$

$\therefore$ Volume of the tube-well $=\pi r^{2} h=\frac{22}{7} \times\left(\frac{3}{2}\right)^{2} \times 280=1980 \mathrm{~m}^{3}$

Rate of sinking the tube-well = ₹ 15 per cubic metre

∴ Cost of sinking the tube-well = Volume of the tube-well × Rate of sinking the tube-well = 1980 × 15 = ₹ 29,700

Thus, the cost of sinking the tube-well is ₹ 29,700.

Inner curved surface of the tube-well $=2 \pi r h=2 \times \frac{22}{7} \times \frac{3}{2} \times 280=2640 \mathrm{~m}^{2}$

Rate of cementing = ₹ 10 per square metre

∴ Cost of cementing the inner curved surface of the tube-well

= Inner curved surface of the tube-well × Rate of cementing

= 2640 × 10

= ₹ 26,400

Thus, the cost of cementing the inner curved surface of the tube-well is ₹ 26,400.