Question 71

Three pipes are made of different shapes. The cross-sections of the pipes are an equilateral triangle, a hexagon and a circle. The perimeter of each of these cross-sections is equal. The flow through the pipes is proportional to the area of cross section. If it takes 8 minutes for the triangular pipe to fill up the tank, what will be the difference in the times taken by the hexagonal and circular pipes?

Solution

Let the sides of triangle be a, that of hexagon be b and circle be c.

Given:

3a = 6b = 2πr

Given: flow rate is proportional to area, so, Flow rate(F) = k Area

Area of triangle = √3/4 a^2

Area of hexagon = 3√3/8 a^2

Area of circle = πr^2 = 9a^2/4π

If triangular pipe takes 480 seconds, hexagonal and circular pipe will take 320 and 290 seconds.

Required difference = 30 seconds = 0.5 minutes.

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