Question

A well of diameter 3 m is dug 14 m deep. The Earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

• A. 4.25 m
• B. 2.250 m
• C. 1.125 m
• D. 1.750 m

Hint:

Volume of earth removed = Volume of embankment. Area of ring = \(\pi(R^2 - r^2)\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Volume of earth dug from well = Volume of cylindrical well.
This earth forms an embankment which is a hollow cylinder (ring).

Step 2: Detailed Explanation:
Well: radius \(r = \frac{3}{2} = 1.5\) m, depth \(h = 14\) m.
Volume of earth = \(\pi r^2 h = \pi × (1.5)^2 × 14 = \pi × 2.25 × 14 = 31.5\pi\) m³.
Embankment: inner radius = well radius = 1.5 m, outer radius = \(1.5 + 4 = 5.5\) m.
Area of ring = \(\pi(R^2 - r^2) = \pi(5.5^2 - 1.5^2) = \pi(30.25 - 2.25) = 28\pi\) m².
Height of embankment \(H = \frac{\text{Volume}}{\text{Area}} = \frac{31.5\pi}{28\pi} = \frac{31.5}{28} = 1.125\) m.

Step 3: Final Answer:
Height of embankment = 1.125 m.