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.

• A. $12.8$ m
• B. $18.2$ m
• C. $15.8$ m
• D. $19.5$ m

Answer 1

The correct option is A $12.8$ m

This embankment is like a larger circle around a circle.

So, the volume of the embankment is the volume of a cylinder with a base area of the larger circle minus a cylinder with a base area equal to the tank's area.

Radius of outer edge of embankment is $=$ $2+1=3$

Radius of inner edge of embankment $=$ $1$

The volume of a cylinder $=\pi r^{2}h$

$\text{V of embankment}=\pi (3m{)}^2\times 1.6-\pi (1m{)}^2\times \left(1.6\right)=12.8{\text{m}}^3$

Since this volume is the same as the tank, then $V=$$\pi r^{2}h$

$\Rightarrow 12.8=\pi r^{2}h$

$\Rightarrow h=\frac{12.8}{\pi r^2}$

$\Rightarrow h=\frac{12.8\pi m^3}{\pi (1m{)}^2}$

$\Rightarrow h=\frac{12.8\pi m^3}{\pi (1m{)}^2}$

$\Rightarrow h=12.8$ m

So, the tank is $12.8$ meters deep.