Question

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?

• A. 45 seconds
• B. 1 minute
• C. 0.5 minute
• D. 7.9 minutes

Answer 1

The Correct Option is C

Let's Assume the sides of triangle be a, the sides of hexagon be b and circle be c.
Given in the question that: 3a = 6b = 2πr
Given: flow rate is proportional to area, so, Flow rate(F) = k Area
Area of triangle = \(\frac{√3}{4a^2}\)
Area of hexagon = \(\frac{3√3}{8a^2}\)
Area of circle = \(\pi\)r² = \(\frac{9 a^2}{4\pi}\)
So, triangular pipe takes 480 seconds, than, the hexagonal and circular pipe will take 320 and 290 seconds.
The difference will be = 30 seconds = 0.5 minutes.
The correct option is (C)