Hi! I worked out my answer but when I double-check the volume with the dimensions I found for the cylinder, it doesn't give me the right volume 1729cm^3. I'm not sure how to fix this, any help would be greatly appreciated. The volume has to be 1729cm^3 and the dimensions i found are r = 6.5cm and h = 13.0cm
Here's my process:

Surely you are getting approximately 1729 with these values? 6.5 and 13 are only approximations.
If you want a volume exactly equal to 1729 you'll have to give:

its pretty far from 1729, v = pi x (r^2) x h
= pi x 6.5^2 x 13
=1725.5 which is a whole 4 cm off!
I think i might just double check with my teacher to see if this is ok. I really appreciate you taking your time to help me, thanks a bunch!!