# Solving for a variable help.

#### Dylonjames5

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

Thank you!

#### Subhotosh Khan

##### Super Moderator
Staff member
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

##### Senior Member
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?