The rain falls on a roof 20 m long and 16.5 m wide and the rainwater is allowed to be stored in a cylindrical tank 8 m in diameter. If it rains 8 cm on a day what is the rise in the water level of the tank due to it?

Given :

The rain falls on a roof 20m long and 16.5 m wide.

It rains 8 cm a day.

To do :

We have to find a rise in the water level.

Solution :

Volume of water collected $= 20 \times 16.5 \times 0.08 m^3 (8 cm = 0.08 m)$

                                                $= 26.4 m^3$

The rainwater is allowed to be stored in a cylindrical tank 8 m in diameter.

Radius $= \frac{8}{2} m = 4 m$

Let the height of the water raised to be 'h' m.

This implies,

Volume of water in the cylindrical tank $= \frac{1}{3} \times 3.14 \times 4 \times 4 \times h m^3$

$\frac{1}{3} \times 3.14 \times 4 \times 4 \times h m^3  =  26.4 m^3$

$16.75 \times h = 26.4$

$h = \frac{26.4}{16.75}$

$h = 1.58 m$

The rise in the water level is 1.58 m.

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Updated on: 10-Oct-2022

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