Question

A drum is in the shape of a frustum of a cone. Its top and bottom radii are $20$ ft and $10$ ft respectively. Its height is $15$ ft. It is fully filled with water. This water is emptied into a rectangular tank. The base of the tank has the dimensions $100$ ft $\times 50$ ft. Find the rise in the height of the water level in the tank.

• A. $1.9$ ft.
• B. $2.1$ ft.
• C. $2.2$ ft.
• D. $2.4$ ft.

Answer 1

The correct option is C $2.2$ ft.

Let $h$ be the height and $R$ and $r$ be the radii of the lower and upper ends of a frustum of a cone.

Volume of a frustum of a cone $=\frac{1}{3}\pi h(R^2+r^2+Rr)$
Hence, volume of the drum $=\frac{1}{3}\times \frac{22}{7}\times 15({20}^2+{10}^2+20\times 10)$

$=11,000{ft}^3$
As this water is emptied into a cuboidal tank, volume of water in tank till height $h=11,000{ft}^3$
Volume of a cuboid of length $\left(l\right)$, breadth $\left(b\right)$ and height $\left(h\right)$ $=l\times b\times h$
So, $100\times 50\times h=11,000$

$\Rightarrow h=2.2ft$