   SEARCH HOME Math Central Quandaries & Queries  Question from Tom, a student: My question is this I know the equations for the final answer but the book skips how to get to one section of the equation.  Q=(a)(v) A= The cross-sectional area of the conduit in square feet (ft2).  So if you have a 5 inch hose how do they get A=0.136 ft2 ? And I know the velocity already v= velocity in ft per second. Hi Tom.

A fire hose has a round cross section, so that's a circular area.

The area of a circle is π r2. The diameter of your hose is 5 inches, so the radius is half of that: 2.5 inches.

That makes the cross-sectional area A = π (2.5 inches)2 = 19.63 inches2.

Since 1 foot = 12 inches, we see that 12 foot2 = 122 inches2.
So there are 144 square inches in a square foot.

This means to convert from 19.63 inches2 to feet2, we divide by 144:

19.63 ÷ 144 = 0.136

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.