The ratio of the rate of flow of water through pipes varies inversely, as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes of diameter 2 cm and 4 cm?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4 : 1
“Varies inversely as the square of the radius” means rate of flow \(\propto\frac{1}{r^2}\): the pipe with the larger radius has the smaller rate.
The rule uses the radius, which is half the diameter: \(2\div2=1\,\mathrm{cm}\) and \(4\div2=2\,\mathrm{cm}\)
Each rate is 1 over the square of its radius: \(\displaystyle \frac{1}{1^2}:\frac{1}{2^2}=1:\frac{1}{4}=4:1\)