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
The shape of the well will be cylindrical.
Depth (h1) of well = 14 m
Radius (r) of the circular end of well = 3/2 m
Width of embankment = 4 m
As per the question,
Our embankment will be in a cylindrical shape having outer radius (R)as 11/2 m and inner radius (r) = 3/2 m
Let the height of embankment be h2
Volume of soil dug from well = Volume of earth used to form embankment
πr2 × h1 = π × (R2 – r2) × h2
⇒ π × (3/2)2 × 14 = π × [(11/2)2 – (3/2)2] × h
⇒ 9/4 × 14 = 112/4 × h
⇒ h = 9/8 = 1.125 m
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