Question

The rain water from a roof of dimensions $22m\times 20m$ 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 fills the cylindrical vessel, then find the rain fall in cm.

Answer 1

Length of the roof,l= 22m
Breadth of the roof,b= 20m
Let the height of water on the roof be h m.
Radius of the cylindrical vessel, r
Height of water in the cylindrical vessel,H= 3.5m
Volume of water falling on the roof = Volume of water in the cylindrical vessel

$lbh=\pi r^{2}H$

$22\times 20\times h=\pi \times 1^2\times 3.5$

$h=\frac{1}{40}m=2.5cm$

Thus, 2.5 cm of rainfall falls on the roof.