Question

A water well has height h meters and diameter 21 m. The cost of plastering the well is ₹1,36,125 at the rate of ₹275/m², then find the height of the well. (∏=22/7)

• A. 2.25 m
• B. 5.5 m
• C. 7.5 m
• D. 4.5 m

Answer 1

Answer:

A. 2.25 m

We are plastering the inner curved surface of the well (a cylinder).

Surface area of cylinder

Curved surface area = $( 2\pi r h )$

Here, diameter = 21 m ⇒ radius ( r = 10.5 ) m

Use cost formula

$\text{Cost} = \text{Area} \times \text{rate}$

$136125 = 2 \times \frac{22}{7} \times 10.5 \times h \times 275$

Simplify

$2 \times \frac{22}{7} \times 10.5 = 66$

So,
$136125 = 66 \times h \times 275$
$136125 = 18150h$

Solve

$h = \frac{136125}{18150} = 7.5$

Final Answer:

Height of the well = 7.5 m