Question

A 14 m deep well with inner diameter 10 m is dug and the earth taken out is evenly spread all around the well to form an embankment of width 5 m. Find the height of the embankment.

Answer 1

Radius of the well (r₁) = 5 m

Depth of the well (h) = 14 m

Width of the embankment = 5 m

Outer radius (R) = 5 + 5 = 10 m

Let the height of the embankment be H

Volume of Earth in the embankment = Volume of the well

πH(R² – r²) = `pi"r"_1^2"h"`

H(10² – 5²) = 5 × 5 × 14

H(100 – 25) = 5 × 5 × 14

H = `(5 xx 5 xx 14)/75`

= 4.67 m

Height of the embankment = 4.67 m