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 32 feet and the child ride has a radius of 24 feet, what is the ratio between the volumes of each ride?

4:3

16:9

64:27

12:9

Question

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 32 feet and the child ride has a radius of 24 feet, what is the ratio between the volumes of each ride? 

 4:3 

 16:9 

 64:27 

 12:9

anonymous · Answer

You must find the volume of each cone. The volume of a cone is given by the equation:$$V=(1/3)\pi r^2h$$
Where r = the radius, and h = the height of the cone.

Because the two rides are only different in radii, the height is constant between both cones.

So the ratio is $$V _{Adult}/V _{Child}$$
or
$$[(1/3)\pi (32)^2h]/[(1/3)\pi (24)^2h]$$
Notice that the h's cancel, then simplify the numerator and denominator.