Math CentralQuandaries & Queries


Question from Vanessa, a student:

Why do we need to find the surface area of a fire hose (cylinder).

Hi Vanessa.

If you are making a fire hose, you need to know how much material you need. Fire hoses are actually quite complicated, with many layers of different materials, but if we simplify things just to a single layer of canvas, we want a certain length of hose and a certain diameter so that the right amount of water reaches where it needs to reach. The amount of canvas is the surface area.


Another example of a cylinder: say your summer job is to paint the outside of those big industrial oil tanks. How much paint do you need? A pail of paint will cover a certain amount of area, so you need to know the surface area of the tank.

Surfaces can be viewed from inside a cylinder too. Consider a scuba diver's air tank, which is also cylindrical. They will explode if the pressure inside is too high. Did you know that pressure is the amount of force per unit area? That's why a common air pressure measurement is pounds per square inch. The area that is measured to make sure that these things don't explode is the inside surface area of the tank. Without knowing that, you wouldn't know what the safe limit of pressure is and how much air you could pump into it without a rupture.

scuba tank

When things warm up or cool down in their environments, it is the surface area that helps determine how quickly this happens. So the surface area of a thermos bottle is very important. The more surface area this cylinder has, the worse it will be at keeping its contents at the original temperature.


This goes for food too. Say you are using your barbecue and you have a footlong hot dog and a thick sausage (both cylinders). If they both contain the same amount of meat, which one will cook faster? The hot dog will, because a long thin cylinder has more surface area than the sausage.


So the surface area of a cylinder, whether you learn it or not, comes up in all kinds of everyday objects. That's why we think it is important to know.

Stephen La Rocque.>

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