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

$$V=\dfrac{1}{3}\pi r^2h$$

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

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

$$k^2=\dfrac{8}{9}$$

$$k=\dfrac{2\sqrt{2}}{3}$$

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