A well of inside diameter 10 m is dug 14 m deep. The earth taken out of it is spread evenly all round it to a width of 5 m to form an embankment. The height of the embankment will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4.66 m
The earth dug out becomes the embankment, so the volume of the embankment equals the volume of the well. The embankment is a ring around the well (a hollow cylinder): inner radius 5 m, outer radius 5 + 5 = 10 m.
Volume of the well \(=\pi r^2h=\pi\times5^2\times14=350\pi\) m3
Area of the ring \(=\pi(10^2-5^2)=75\pi\) m2
Height of the embankment \(\displaystyle=\frac{350\pi}{75\pi}=\frac{14}{3}=4.66\ldots\) m