Find the cost of sinking a tube well 280 m deep, having diameter 3 m at the rate of Rs 3.60 per cubic metre.
Question:

Find the cost of sinking a tube well 280 m deep, having diameter 3 m at the rate of Rs 3.60 per cubic metre. Find also the cost of cementing its inner curved surface at Rs 2.50 per square metre.

Solution:

Given data is as follows:

Height of the tube well = 280 m

Diameter = 3 m

Rate of sinking of the tube well $=$ Rs. $3.60 / \mathrm{m}^{3}$

Rate of cementing $=$ Rs. $2.50 / \mathrm{m}^{2}$

Given is the diameter of the tub well which is 3 metres. Therefore,

r = 3/2 m

Volume of the tube well $=\pi r^{2} \mathrm{~h}$

= 22/7 × 3/2 × 3/2 × 280

$=1980 \mathrm{~m}^{2}$

Cost of sinking the tube well = Volume of the tube well × Rate of sinking the tube well = 1980 × 3.60

= Rs. 7128

Curved surface area = 2πrh

= 2 × 22/7 × 3/2 × 280

$=2640 \mathrm{~m}^{2}$

Cost of cementing = Curved Surface area × Rate of cementing

= 2640 × 2.50

= Rs. 6600

Therefore, the total cost of sinking the tube well is Rs.7128 and the total cost of cementing its inner surface is Rs. 6600.