Solving for a variable help.

[Dylonjames5]

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



Thank you!

 

[Subhotosh Khan]

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.....

 

[Denis]

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?