Too many unknowns

Monster Kid

Hi all, I was wondering if I could get some help with a question I've been mulling over for a while. Yes it's homework! but I've been working away at it for ages and it's just not coming right for me!
Question : A rectangular box is designed such that its length is twice its height and its width is 1cm greater than its height.
(i) Find the volume of the box in terms of h.

I had no problem with this : 2h^3+2h^2

(ii) If the volume of the box is 300cm^3, find the value of h.

This is the bit I'm having a problem with. I know that 2h^3+2h^2=300cm^3, length=2h, and width=h+1, but I just can't seem to work backwards from that to find h. Having three unknown l*h*w=300 is putting me off, because usually questions give you either l, h, or w.

Thank you for any help offered.

LeixlipRed

You don't have three unknowns.

You have the expression:

2h^3+2h^2=300

You can use this to solve for h. It's a cubic equation, any idea where you'd go next?

Monster Kid

Lights were on but nobody was home! Cubic equation -> so I can substitute in f(1), f(2) etc. I found h=5cm, length=10cm and width=6cm.

Thanks for your help