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.

Answer 1

Height of the tube-well, h = 280 m

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

∴ Volume of the tube-well = $\mathrm{\pi }{r}^{2}h=\frac{22}{7}\times {\left(\frac{3}{2}\right)}^2\times 280$ = 1980 m³

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 = $2\mathrm{\pi }rh=2\times \frac{22}{7}\times \frac{3}{2}\times 280$ = 2640 m²

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.