Question on Radius of Cylindrical Vessel

Topic : Radius of Cylindrical Vessel

Question : The rain water from a roof of 22 inches * 20 inches drains into a cylindrical vessel having diameter of base 2 inches and height 3.5 inches.If the vessel is just full, find the rainfall in inches.

Solution :
r = Radius of cylindrical vessel = 1 inches
h = Height of cylindrical vessel = 3.5 inches
Volume of cylindrical vessel = pi * r2 * h
= (22/7) *12 * 3.5 = 11 inches
Let the rainfall be x inches.Then,
Volume of the water = Volume of a cuboid of base 22 inches * 20 inches and height
x inches
= 22 * 20 * x cubic inches
Since the vessel is full of water that drains out of the roof into the vessel.
Volume of water = Volume of the cylindrical vessel
22 * 20 * x = 11
x = 11 / (22 * 20 ) = 2.5 inches