What is the ratio of times taken to fill the two drums

Question

Suppose a hose pipe supplies water at a fixed rate. There are two oil drums each in the shape of a circular cylinder. The larger drum is twice the height and the base has twice the diameter compared to the small drum. What is the ratio of times taken to fill the two drums

Answer 1

Let Q = water flow rate (ft³/min)

d = diameter of the first barrel (ft)

h = height of the first barrel (ft)

V₁ = volume of first barrel = (pi*d²*h)/4 (ft³)

V₂ = volume of the second barrel = pi*(2d)²*(2h) = (2*pi*d²*h) (ft³)

Then, T₁ = Time to fill first barrel = V₁/Q = (pi*d²*h)/4Q (min)

T₂ = Time to fill second barrel = V₂/Q = (2*pi*d²*h)/Q (min)

The ratio T₁/T₂ = 1/8 or T₂ = 8T₁