Answer to Question #223294 in Geometry for Rashinda

Question

The radius and height of a cone are respectively r and h. If the height is multiplied by 9/2; by what fraction should the radius be multiplied so as to quadruple the cones volume?

Answer 1

$V=\dfrac{1}{3}\pi r^2h$ $4V=\dfrac{1}{3}\pi (kr)^2(\dfrac{9}{2}h)$ $\dfrac{\dfrac{1}{3}\pi (kr)^2(\dfrac{9}{2}h)}{\dfrac{1}{3}\pi r^2h}=4$ $k^2=\dfrac{8}{9}$ $k=\dfrac{2\sqrt{2}}{3}$ $k=\dfrac{2\sqrt{2}}{3}$

The radius should be multiplied by $\dfrac{2\sqrt{2}}{3}.$

$\dfrac{2\sqrt{2}}{3}.$