Question

A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embankment 2 m in width and 1.6 m in height. Find the depth of the circular tank.

Answer 1

Given, diameter of circular tank = 2 m

And width of embankment = 2 m

Height = 1.6 m

Radius of tank = `2/2` = 1 m

Outer radius of embankment = 1 + 2 = 3 m

∴ Volume of earth = π(R² – r²) × h

= `22/7 (3^2 - 1^2) xx 1.6  m^3`

= `22/7 xx (9 - 1) xx 1.6  m^3`

= `22/7 xx 8 xx 1.6  m^3`

= `22/7 xx 12.8  m^3`

Now volume of the earth dug out from the tank

= `22/7 xx 12.8  m^3`

Radius of tank = 1 m

∴ Depth of circular

= `"Volume"/(pir^2)`

= `(22 xx 12.8 xx 7)/(7 xx 22 xx 1 xx 1)`

= 12.8 m