# The formula for the volume of a cone is V= 1/3 pi r^2h with pi =3.14 . How do you find the radius, to the nearest hundredth, of a cone with a height of 5 in. and a volume of 20" in"^3?

$h \approx 1.95 \text{ inch (2dp).}$
$V = \frac{1}{3} \pi {r}^{2} h \Rightarrow {r}^{2} = \frac{3 V}{\pi h} \Rightarrow r = \sqrt{\frac{3 V}{\pi h}} .$
With, $V = 20 \mathmr{and} h = 5 , r = \sqrt{\frac{\left(3\right) \left(20\right)}{5 \pi}} = \sqrt{\frac{12}{\pi}}$
$= \sqrt{3.8197} \approx 1.95 \text{ inch (2dp).}$