Solving for a variable help.

Could someone help me figure out how to solve for r?

View attachment 11052

Thank you!
\(\displaystyle \displaystyle{42.9 \ = \ \pi*\left[\dfrac{r^2*h}{3} - \dfrac{r^2(h \ - \ 7.72)^3}{3h^2}\right]}\)

\(\displaystyle \displaystyle{42.9 \ = \ \pi*\dfrac{r^2}{3}\left[ h \ - \dfrac{(h \ - \ 7.72)^3}{h^2}\right]}\)

continue.....
 
Suggestion to "shorten/simplify" the job:
let u = 42.9/pi and v = (h - 7.72)^3

So you now have:
u = r^2(h) / 3 - r^2(v)/(3h^2)

Solve for r.
Substitute back in if necessary.
Get my drift?
 
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