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?

options:
25:4

15:6

125:8

5:2

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 25 feet and the child ride has a radius of 10 feet, what is the ratio between the volumes of each ride?

options:
25:4

 15:6

 125:8

 5:2

anonymous · Answer

please help

hero · Answer

Just use the formula for volume of a cone to find the ratio:

$$\frac{\text{Volume of Cone One}}{\text{Volume of Cone Two}} = \frac{\pi r^2h/3}{\pi r^2h/3} = \frac{\pi (25)^2h/3}{\pi(10)^2h/3}$$

Basically, everything cancels except

$$\frac{25^2}{10^2}$$

If you simplify that, you might get one of your answer choices.

anonymous · Answer

thanks @Hero

hero · Answer

Did you figure  out which answer choice is correct?

anonymous · Answer

wait i got 6.25 and thats not any of my choices @Hero

hero · Answer

That's because you simplified it to a decimal form rather than fraction form.

jdoe0001 · Answer

rationalize 6.25

anonymous · Answer

so wat would it be in fraction?

jdoe0001 · Answer

hmm, so you're doing rations and dunno how to simplify fractions?

anonymous · Answer

no thats y i need help

hero · Answer

$$\frac{25^2}{10^2} = \left(\frac{25}{10}\right)^2 = \left(\frac{5 \times 5}{5 \times 2}\right)^2 = \left(\frac{5}{2}\right)^2 = \frac{25}{4}$$

anonymous · Answer

ohh i get it now
thanks a lot