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Question
A rectangular water tank of base 11 m × 6 m contains water upto a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.
Solution
Volume of water in tank = Volume of cuboidal tank up to a height of 5 m
According to the question,
For cuboidal tank
Length, l = 11 m
Breadth, b = 6 m
Height, h = 5 m
We know that the equation to find the volume of the tank,
Volume of tank = lbh, where, l, b and h are the length, breadth and height of tank respectively
Volume of water = 11(6)(5) = 330 m3
We also know that,
Base radius of cylindrical tank, r = 3.5 m
Let the height till which the cylindrical tank is filled = h m
Hence, using the formula,
Volume of a cylinder = πr2h, where r is base radius and h is the height of cylinder
Volume of water in cylindrical tank = π(3.5)2h
330 m3 = `22/7 xx 3.5 xx 3.5 xx "h"`
330 m3 = h × 38.5
h = 8.57 m
Hence, the height till which the cylindrical tank is filled = 8.57 m
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