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

Answer 1

Do you know how to find the volume of a cone?

Answer 2

1/3*pi*r^2*h

Answer 3

So we're assuming the two cones are the same height, which means the only thing that changes is the radius.

Answer 4

Now, if we look at the radii, we have a ratio of 32:24, right?

Answer 5

yes

Answer 6

we can reduce it

Answer 7

Yep yep. But! The ratio of the areas is not proportional to the radii, it's proportional to the radii *squared*. So if you square the radii, what do you get?

Answer 8

32^2 =1024
24^2 = 576

Answer 9

equaling 16:9

Answer 10

Yepper! There is actually an easier way. If you'd simplified the original 32:24 ratio, you could get 4:3. Then you can square that ratio and get 16:9 as well :)

Answer 11

that sounds more complicated. >.<

Answer 12

@shadowfiend thanks again. you rock. maybe u should be a teacher

Answer 13

Haha. I was a Teaching Assistant for a while in college. But I'd rather build this site so everyone can be a teacher :)

Answer 14

your one of the builders of this site. thats sweet

Answer 15

Yep yep :)