Question

the rain water collected on the roof of a building of dimensions 22 m ×20 m is drained into a cylindrical vessel having base diameter 2m and height 3.5 m. if the vessel is full upto the brim find the height of rain water on the roof.

Answer 1

Given,

The dimensions of the roof of a building is 22 metres × 20 metres.

Base diameter of the cylindrical vessel = 2 metres

Height of the cylindrical vessel = 3.5 metre

To find,

The height of the rainwater on the roof.

Solution,

The base diameter of the vessel = 2 metres

The base radius of the vessel = 2/2 = 1 metre

The volume of the vessel = π × (1)² × 3.5 = 22/7 × 3.5 = 22/2 = 11 m³

The volume of the water = 11 m³

Let,the height of the rainwater in the roof = x metres

So,the volume of the water = 22×20×x = 440x m³

Now, if you compare the two values of the volume of the water,then we will get the following mathematical equation,

440x = 11

x = 11/440

x = 0.025

Hence,the height of the rainwater in the roof is 0.0025 metre.