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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.
Solution
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
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