Question

The volume of a cylinder increased by 8 times the original volume. How many times greater are each of the dimensions of that new cylinder?

2

3

4

8

Answer 1

Volume of a cylinder: \(\large V_{\text{old}}=\pi {r_{\text{old}}}^2h_{\text{old}}\)

The volume is scaled up by a factor of 8: \(\large V_{new}=8\pi {r_{\text{old}}}^2h_{\text{old}}\)

You want to be able to factor the constant 8 so that you can distribute it to the old radius and height:
\(\large V_{new}=8\pi {r_{\text{old}}}^2h_{\text{old}}=2\times2^2{r_{\text{old}}}^2h_{\text{old}}=\pi{(2r_{\text{old}})}^2(2h_{\text{old}})\)
This means the new radius is twice the old radius, and the new height is twice the old height.