The volume of a cone varies jointly as the square of its radius and its height. (V=k*r^2*h) If the volume of a cone is 9pi inches when the radius is 3 inches and its height is 3 inches, find the volume of a cone when the radius is 5 inches and the height is 9 inches. Express the answer in terms of pi. Given answer is 75 pi. How do I work this?

Please help? Anyone?

Question

The volume of a cone varies jointly as the square of its radius and its height.  (V=k*r^2*h) If the volume of a cone is 9pi inches when the radius is 3 inches and its height is 3 inches, find the volume of a cone when the radius is 5 inches and the height is 9 inches.  Express the answer in terms of pi.  Given answer is 75 pi.  How do I work this?

Please help?  Anyone?

hoblos · Answer

first you need to calculate k

you have   V=k*r^2*h

so  9pi = k*3^2*3

so what's k ?

anonymous · Answer

that's where I am having the problem.

anonymous · Answer

If I could figure out the k, I'd be halfway to figuring this out.  The other half is trying to figure out how to express the answer in terms of pi

anonymous · Answer

because I have another question exactly like it, and i feel like I am overlooking something incredibly simple

hoblos · Answer

$$9 \pi = k*3^2*3$$
$$k = \frac{ 9 \pi }{ 3^2*3 }$$

hoblos · Answer

to express the answer in terms of pi, you have to keep k in terms of pi

anonymous · Answer

how do I do that?

hoblos · Answer

you just keep the pi and simplify the rest
so
$$k = \frac{ 9 }{ 9*3 } \pi$$

hoblos · Answer

can you simplify it ?

anonymous · Answer

k = 1/3 π

hoblos · Answer

correct

anonymous · Answer

hmmm....

hoblos · Answer

you didn't understand ?

anonymous · Answer

actually am trying to figure out how to plug the same value into another equation.  want to see if the k i got from this answer will also be the same in the other question

hoblos · Answer

actually for a cone k is always  1/3 pi
but that's only for a cone
you can use this k to find the volume of the other cone mentioned in this question "radius is 5 inches and the height is 9 inches"

anonymous · Answer

you're a life saver!  i wish I could give you 2 medals for this question.

anonymous · Answer

since the other question is also about a cone, then yes, I can do the math and move on.  i simply could not figure out how to manipulate the math to make pi behave

hoblos · Answer

so you are able to do it now ?

anonymous · Answer

let me see.  V=1/3 *r^2*h
my next question is 
?π=1/3*4^2*3

hoblos · Answer

|dw:1395627439545:dw|

anonymous · Answer

1/3π*4^2*3
1/3π*16*3
wouldn't the 1/3 and the 3 cross cancel each other out and leave me with 16π?

hoblos · Answer

yeah correct

anonymous · Answer

thankee-sai!

hoblos · Answer

glad to help! :)

anonymous · Answer

now let's see if I can manage to pull off a somewhat passing grade on this test :/

hoblos · Answer

i hope you can