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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.

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1.9

2.1

2.2

2.4

answer is C.

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Detailed Solution

It is given top and bottom radii

20

ft and

10

ft respectively and height

15

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} πh (R^{2} + r^{2} + Rr)

So, volume of the drum

= \frac{1}{3} \times \frac{22}{7} \times 15 (20^{2} + 10^{2} + 20 \times 10)

\Rightarrow \frac{22}{7} \times 5 (400 + 100^{} + 200)

\Rightarrow \frac{22}{7} \times 5 \times 700

\Rightarrow 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

(l)

, breadth

(b)

and height

(h)

= l \times b \times h

So,

100 \times 50 \times h = 11, 000

\Rightarrow h = \frac{11000}{5000}

\Rightarrow h = 2.2 ft

Therefore, height of the water level in the tank

2.2 ft

.
Hence, the correct option is 3.

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