Volume of a Cylinder

Finding the volume of a cylinder is relatively easier than what it looks, mostly because the pi symbol can confuse us. But I'm going to take you through a few step by step guides to help you analyse what to do.

Step 1: Firstly, find the area of the cross-sectional shape. Now in a cylinder the cross-sectional shape is a circle and so the formula to find the area is a=πxr squared where π represents pi (often in papers you must accept the value of pi to be 3.1416 if you don't have the symbol on your calculator, unless told otherwise) and r squared is represented by the radius multiplied by itself.

Note: It is usually easier to leave the answer to this step in the form of pi.

Step 2: Now you have the answer for the area of the cross sectional shape, but that shape is 2D when the cylinder is 3D. This is easily mended though. Find the length of the cylinder and multiply it by the area of the cross-section (the answer from above). There you go you now have the volume of the cylinder.

So overall formula is the area of the cross sectional shape multiplied by the length of the object. Now this works with most 3D objects such as cuboids or triangular prisms.

Note: Often in the non-calculator papers you are not expected to write it as a decimal so you may leave it in the form of π: e.g. 49π, or 13π, or √5π. However in calculator papers you maybe asked to give the answer to a certain number of decimal places; your calculator may give you an answer like that in the form of pi, so simply click the button with the S <=> D on it to get the decimal answer.

If you're having a hard time remembering the formula there's a nice little trick to help you. Just use pizza to help you; yes, for once that greasy Italian food is good for you. If you substitute the value for the radius with the letter z and the value for length with a the formula should look a bit like this:

Pi x z x z x a = π x the radius (z) multiplied by itself x height (a)

Pizza

So an example:

Sarah had a pack of eight cylindrical batteries; the radius of the batteries were 5mm and each battery is 4cm long. What was the volume that the batteries occupied?

If it helps you can underline or take out important pieces of information from the question:

BATTERIES: 8 RADIUS: 5mm LENGTH: 4cm or 40mm

AREA OF CROSS-SECTION

Area = π x r squared

Area = π x (5x5)

Area = 25π

VOLUME OF ONE BATTERY

Area x length = Volume

25π x 40 = Volume

1000πmm = Volume or 3141.592654...mm or 3141.59(to 2 d.p.)

VOLUME OF EIGHT BATTERIES

3141.59 x 8 = 25,132.72 (to 2 d.p.)mm

Here's an example for you to try:

John has a cylindrical iron pipe. The diameter of the pipe is 6cm whilst the length of the iron pipe is 60cm.

a) What is the area of the cross-section?

b) What is the complete volume of the pipe?

c) John finds another pipe that has the same diameter but is twice the length of the previous pipe. He wields the two pipes together. Accepting that when wielding there are no changes to the lengths of the two pipes, what is the volume of the new pipe?