A well with an internal diameter of 8 m is dug to a depth of 12 m. The earth taken out of it is spread all around the well to a width of 8 m to form an embankment. What is the height (in m) of the embankment?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1, i.e., 1.5.
Radius of well, r = 8 ÷ 2 = 4 m
Depth of well, h = 12 m
Volume of earth = Volume of cylinder = π × r2 × h = π × 42 × 12 = π × 16 × 12 = 192 π m3
Width of embankment = 8 m → outer radius = 4 + 8 = 12 m
Let the height of the embankment = H
Volume of embankment = π × (outer radius2 − inner radius2) × H = π × (122 − 42) × H = π × (144 − 16) × H = 128 π × H
Equate volumes: 192 π = 128 π × H → H = 192 ÷ 128 = 1.5 m