Question

A well with inner radius 4m is dug 14m deep earth taken out of it has been spread evenly all around a width of 3m it to form an embankment. Find the height of the embankment?

Answer 1

Given that inner radius of a well (a)= 4am

Depth of a well (h) = 14m

Volume of a cylinder = πr²h

V1 = π(4)² x 14cm³      .................(1)

Given well is spread evenly to form an embankment

Width of an embankment = 3m

Outer radii of a well(R) = 4 + 3 = 7m.

Volumeof a hollow cylinder `=pi(R^2-r^2)xxhm^3`

`V_2=pi(7^2-4^2)xxhm^3`      ............(2)

Equating (1) and (2)

V₁ = V₂

⇒ `pi(4)^2xx14=pi(49-16)xxh`

⇒ `h=(pi(4)^2xx14)/(pipi(33))`

h = 6.78m