15 Volume of a Cylinder
Click play on the following audio player to listen along as you read this section.
What do you think is in the tank in the picture to the left?
Maybe water? Maybe grain? Maybe old math textbooks for the construction trades?
For us right now, it’s less important to know what is in the tank and more important to know how to figure out how much stuff can fit into the tank.
This type of tank in known as a cylinder and is comprised of three basic parts. It has a top, a bottom, and a middle section. We will assume that the top and the bottom are both perfect circles with equal diameter and equal area.
A good example of a cylinder would be a hot water tank. Take a look at the hot water tank to the right and ask yourself what you might need to know if you were required to calculate the volume of the tank.
What did you come up with? How about trying your hand at coming up with a formula. I’ll give you one hint before you give it a shot.
Hint: Volume is in cubic form. For example: cubic feet, cubic metres, cubic inches, etc.
Formula for Volume of a Cylinder
Here’s the formula.
[latex]\Large \text{volume of cylinder} = {\text{diameter}}^{2} \times 0.7854 \times \text{height}[/latex]
Remember that the top of a cylinder is simply a circle. It has a diameter, a radius, and a circumference. The bottom of the tank has the same dimensions as the top of the tank.
So we need this calculation (the area of the top or bottom) to use as a starting point.
The next question that would come about is, “How high or how long is the tank?”
This would also play a big part in calculating the volume.
Put this all together and you get your formula:
[latex]\Large \text{volume of cylinder} = {\text{diameter}}^{2} \times 0.7854 \times \text{height}[/latex]
One last question:
What kind and type of units will we be dealing with in our answer?
Units for Volume of a Cylinder
There are actually two parts to this answer.
Part 1
The answer remains in whatever units the variables are that we are dealing with. So for instance, if we are dealing with feet then our answer would end up being some version of feet. If we are dealing with inches then our answer would end up being some version of inches.
Note that you have two different variables here, diameter and height. Make sure that when working out your answer that both variables are in the same units. If diameter is in inches and height is in feet, you would have to convert one or the other so that they would both be the same unit.
Part 2
As stated earlier, our answer would be in cubic units. Although we have only two variables (diameter and height), the diameter is squared therefore we could write the formula like the following:
[latex]\Large \text{volume} = \text{diameter} \times \text{diameter} \times 0.7854 \times \text{height}[/latex]
In the end, we would actually have three variables with two of them being the same. This is how we get our answer in cubic (3) units.
Examples
A cylindrical tank has a diameter of 7