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Question

The number of litres of water g in a circular tank varies jointly with the square of the radius r2, and the depth d. If g=3016 when r=4 and d=2, find the number of litres in the tank when r=3 and d=1.5

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Solution

It is given that the number of litres of water g in a circular tank varies jointly with the square of radius r and the depth d andg=3016 when r=4 and d=2, therefore,

g=kr2d3016=k×(4)2×23016=k×16×23016=32kk=301632=3774

Thus, the general equation is g=3774r2d.

Since r=3 and d=1.5, therefore,

g=3774×(3)2×1.5=3774×9×1.5=5089.54=1272.375

Hence, 1272.375 litres was there in the tank when radius is 3 and depth is 1.5.

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