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The rainwater from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having a diameter of base 2 m and height of 3.5 m. If the rainwater collected from the roof just fills the cylindrical vessel, then what will be the rainfall in cm?

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2.5 m

5.5 m

3.5 m

2.8 m

answer is A.

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Detailed Solution

It is given that the rainwater from the roof drains into a cylindrical vessel.
The radius of cylindrical vessel =

\frac{2}{2} = 1 m

and height is 3.5 m.
The volume of the roof:
Let us assume the rainfall be x cm, that is

x 100 m

. So,

V = 22 × 20 × x 100 V = 22 x 5 m 3 … … 1

The volume of the cylinder is

π r 2 h

.
The volume in the cylindrical vessel:

V = \frac{22}{7} \times 1 \times 3.5

V = 11 m^{3} . . . . . (2)

Equating both the equations (1) and (2) to find x.

\frac{22 x}{5} = 11

x = \frac{5}{2}

x = 2.5 m

Therefore, 1 is the correct option.

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