Question

The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm

Answer 1

Let the rainfall be 'x' cm [i.e. 0.01x meters because 1 m = 100 cm ] .

For cylindrical vessel,

Diameter of base = 2 m

Base Radius = 1 m

[As radius = diameter/2]

Height, h = 3.5 m

As we know,

Volume of cylinder = πr²h

Where r is base radius and h is height of cylinder.

So,

Volume of cuboidal vessel = π(1)²(3.5)

= 22/7 x 3.5 = 11 m³

Also,

For roof

Length, l = 22 m

Breadth, b = 20 m

Height, h = height of rainfall = 0.01x m

As we know,

Volume of cuboid = lbh

Where l, b and h are length, breadth and height of the cuboid respectively.

Volume of water on roof = 22(20)(0.01x) = 4.4x m³

Given,

Volume of water on roof = volume of cuboidal vessel

4.4x = 11

x = 2.5 cm

Height of rainfall is 2.5 cm.