Math CentralQuandaries & Queries


Question from Carlou:

How many liters of water in a 2.5 inches diameter of fire hose with a 20 meters in length

Hi Carlou,

The volume is the area of the circular cross section times the length. Your cross section is a circle with diameter 2.5 inches which is $2.5 \times 2.54 = 6.35$ centimeters. The area of a circle is $\pi \; r^2$ where $r$ is the radius and hence the area of the cross section is

\[\pi \times \left( \frac{6.35}{2} \right)^2 = 31.7 \mbox{ square centimeters.}\]

Your hose is $20 \mbox{ meters } = 2,000 \mbox{ centimeters long}$

and hence the volume is

\[31.7 \times 2,000 = 63,338 \mbox{ cubic centimeters.}\]

There are 1,000 cubic centimeters is a liter so the volume of water in the hose is 63.3 liters.

I did this assuming the inside diameter of the hose is 2.5 inches. You should check this as a "2.5 inches diameter fire hose" may have an outside diameter of 2.5 inches.


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