How do you solve this A level maths solid of revolution question

I did a past paper and got part b of question 2 wrong. Here is the link to the paper:
http://www.carlgauss.co.uk/PDFs/A-Level%…
I found the answer to 2a to be pi/12
Here's the mark scheme if that helps:
http://www.mathsman.co.uk/C4%20Jan%20200…
10 points to best answer (1st person to answer correctly with a good explanation)

The object in part (b) is geometrically similar and larger to the solid in part (a).

The length between the ends of the original object = 1/2 - (-1/4) = 3/4

The length scale factor = 3/(3/4) = 4

Volume scale factor = (length scale factor)^3 = 64

Larger object volume = 64*pi/12 = 16*pi/3

EDIT. This is almost what is written in the mark scheme. I don't know whether I can add any further explanation. Was it the relationship between volume scale factor and length scale factor that you had forgotten?

If it was 3pi/4 cm high it would have volume pi/12 if you are correct.

Thus if the height is 3cm we scale the height by 4 and the volume by 4^3=64

So the volume is pi*64/12 =pi *16/3 I think.