How does the volume of a cylinder change when its diameter is quadrupled?

Question

How does the volume of a cylinder change when its diameter is quadrupled?

Answer 1

Hi Alex,

You asked, "How does the volume of a cylinder change when its diameter is quadrupled?" Let's take a look at the formula for the volume of a cylinder:

V=Π r²h

One way to answer this is to look at the radius, and reason about what is going to happen to it when you quadruple the diameter. Then remember that you are squaring the radius in the volume formula, so you must then reason about what the radius size increase will do once it is squared.

Another way to find an answer is to substitute real numbers for the radius and height and then compare your results.

Let's suppose we have a cylinder with a radius of 2 units (diameter 4), we would find its volume as follows:

V = Π 2²•6= 24Π ≈ 75.36 units³

If we quadrupled the diameter to 16, then our new radius would be 8. The new volume would be as follows:

V =Π 8²• 6 = 384Π ≈1205.76 units³

We can compare the size of of the second volume 384Π units³ to 24Π units³. How much larger is it? Divide 384 by 24 to find out by what factor you have increased the volume of the cylinder.

I hope this answer helped. If you found it useful, please upvote it.