3 quick problems involving related formulas.

Dec 2014
129
101
USA


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