# Thread: 3 quick problems involving related formulas.

1. ## 3 quick problems involving related formulas.

The main problem I am having with these is that when I replace one variable with another variable, I introduce other variables, values for which I cannot solve! The links to the images are below.
https://scrn.li/2J5l5X0cX7z1Y7
https://scrn.li/XrAH6lKvW7Zf6x
https://scrn.li/xGjxwh2PC8As31

2. ## Re: 3 quick problems involving related formulas.

note that $|BP| = 9-x$

determine $|AP|$ in terms of $x$ using Pythagoras

finally, note that time = distance/rate

let $r$ be the large cone radius

using similar triangles

$\dfrac{2}{h-7} = \dfrac{r-2}{7} \implies r = \dfrac{2h}{h-7}$

finally, note volume of a cone is $V = \dfrac{\pi}{3}r^2 h$

what now?

$r = \dfrac{h}{15} \implies h = 15r$

finish it

3. ## Re: 3 quick problems involving related formulas.

Thank you profusely!