i dont understand how a ratio can be turned into a formula for volume, please help

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[fossil token]

Suppose the ratio of height to radius is k: k = h/r.
We know that V = πr^2 h. So, express h from the ratio and substitute it into the volume formula.

[urban halo]

how does k = h/r?

the height over radius?

[fossil token]

By the statement of the problem we are given the ratio h/r.

[urban halo]

yeah

[urban halo]

oh so no need to cube the ratio?

i was taught that in order to convert a ratio to match a 3d shape, you need to cube it

the volume of a 3d shape*

the ratio is 1 dimensional

i dont understand

[fossil token]

No.

We have:
h/r = k
V = πr^2 h
Express h from the first equation and substitute it into the second.

[urban halo]

what do you mean by express

[urban halo]

what would the answer be?

[fossil token]

Find h from the first equation and substitute it into the second equation.

[urban halo]

so i just substitute 3?

what about the 2

the radius

[fossil token]

No, what?
Again, express h from the equation h/r = k. What do you get?

[urban halo]

2/3

[fossil token]

No.

If h/r = k, then h = kr.

Then, substitute h = kr into V = πr^2 h.

[urban halo]

i see

so height in terms of radius would be

h=3/2r

which you would substitute

into the main formula

3 pi radius cubed over 2

which is B?

[fossil token]

Yes.

[urban halo]

i see

thanbks