Question

You are filling a cylindrical drum (D = 22.5 in., H = 33.5 in.) with water flowing from a garden faucet at a rate of 10 GPM. How long will you have to wait to fill the drum? Express you answer in minutes.

Answer 1

Explanations & Calculations

• Volume of the cylinder

$\qquad\qquad \begin{aligned} \small V&=\small \pi\frac{D^2}{4}H\\ &=\small \pi\frac{(22.5\,in)^2}{4}(33.5\,in)\\ &=\small 13319.9\,in^3\\ &=\small 13319.9\,(0.0254\,m)^3\\ &=\small 0.218\,m^3=0.218\,l\\ &=\small 0.218\times0.264\,gallons\\ &=\small 0.058\,gallons \end{aligned}$

• Then the time taken for the filling at the given rate is

$\qquad\qquad \begin{aligned} \small t&=\small \frac{0.058\,G}{10\,Gpm}\\ &=\small 0.0058\,min\\ &=\small 0.0058\times60\,s\\ &=\small 3.5\,s \end{aligned}$