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

anonymous · Answer

@hartnn

anonymous · Answer

@amistre64

anonymous · Answer

@jhonyy9

amistre64 · Answer

like a cone

adults 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?

Can you define the formula for the volume of a cone?

anonymous · Answer

no I don't know the formal for volume of a cone could u tell me

amistre64 · Answer

i could; but it would be better if you could find it in your material, or at least google it .. that way you have more weighted participation in the process.

anonymous · Answer

surface area

anonymous · Answer

I mean if u tell all I got to do is pug it in right

amistre64 · Answer

if we know the formula, then the rest is just childs play :)

anonymous · Answer

v=1/3b*h

amistre64 · Answer

thats a good formula, but lets be sure about it:  b = base area

anonymous · Answer

ok

amistre64 · Answer

in this case, the adults have a volume of:$$V_a=\frac13\pi~r^2h$$
its similar to some scaled version of:$$V_c=\frac13\pi~(rk)^2~(hk)$$
which is k^3:1 in ratio

amistre64 · Answer

the key now is to determine the scaling factor:

25k = 10

anonymous · Answer

what do I do with 25k=10

anonymous · Answer

solve that

amistre64 · Answer

well, since our ratio is k^3:1,  we need a value for k ... 25 is scaled to 10 by some factor k ...

25k = 10,  solve for k yes

amistre64 · Answer

i spose we could just as easily scaled it from 10 to 25 but the problem alludes to an adult:child ratio instead of the other way around

anonymous · Answer

I got 2.5

amistre64 · Answer

$$k=\frac 1{2.5}~:~or~k=2.5$$
$$k^3=\frac 1{2.5^3}~:~or~k^3=(2.5)^3$$
depending on the how we define the setup i spose

anonymous · Answer

which one would u pick

amistre64 · Answer

hmm, id pick the right side for simplicity:  15.625 to 1

do we have any options to narrow the feild?

amistre64 · Answer

the adult volume is 15.625 times the volume of the childs volume

anonymous · Answer

is that the answer cause my computer froze and I had to cut it off

anonymous · Answer

@amistre64

amistre64 · Answer

thats the results we get, so yes.  It may have to be formated for whatever is grading it tho

anonymous · Answer

25:4 

 15:6 

 125:8 

 5:2

anonymous · Answer

B

anonymous · Answer

right

anonymous · Answer

@amistre64

amistre64 · Answer

not B

this is asking about the ratio of volumes right?

anonymous · Answer

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? 

 25:4 

 15:6 

 125:8 

 5:2

anonymous · Answer

that's whats it asking

amistre64 · Answer

$$\frac13\pi~r^2h\to\frac13\pi~(rk)^2~(hk)$$
$$r^2h\to(rk)^2~(hk)$$
$$r^2\to(rk)^2~k$$
$$1\to k^2~k$$
$$1\to k^3$$
$$r\to rk$$
$$10\to 10k=25;~k=2.5;~k^3=15.625,~15\frac58$$
soo$$1: 15+\frac58$$
$$8: 8(15)+5$$
$$8: 125$$

amistre64 · Answer

125 to 8  then :)

anonymous · Answer

oh thanks

amistre64 · Answer

youre welcome ... the decimal had me for a loop or a second :)

anonymous · Answer

lol