A water ride at a local water park has a ride shaped like a cone that acts like a funnel whereby guests swirl around the cone until they drop through its center. There is one ride for adults and a similar, smaller version for children. If the adult ride has a radius of 25 feet and the child ride has a radius of 10 feet, what is the ratio between the volumes of each ride?

Question

dumbcow · Answer

Volume of cone = 1/3pi*r^2*h
height can be treated as function of radius
so volume is a factor of radius cubed
therefore ratio of volumes is ratio of radii cubed

--> 10/25 = 2/5,   (2/5)^3 = 8/125

mertsj · Answer

$$\frac{V _{1}}{V _{2}}=\frac{\pi25^2h}{\pi10^2h}=\frac{625}{100}=\frac{25}{4}$$

anonymous · Answer

Thanks, guys. :)

mertsj · Answer

yw