# Describing an equation

Which of the following describe this formula correctly: $S = 2\pi rh$

1.S is jointly proportional to radius and height

2.S is directly proportional to radius and height or

3.S varies directly with radius and height.

I am leaning towards choice 3 but I am not 100% positive.

This is stuff on variation that might help. k is a constant

"S varies as x" means S = kx

"S varies jointly as x and y" means S = kxy

"S varies as x + y" means S = k(x + y)

"S varies inversely as x" means S = k/x

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How are the adverbs "jointly" and "directly" defined in your book? – J. M. May 9 '11 at 15:28
I think directly means a constant is being multiplied with 1 variable, jointly means a constant is being multiplied with more than 1 variable. see edit. – Matt May 9 '11 at 15:36
So, why did you choose the third as opposed to, say, the first? – J. M. May 9 '11 at 15:36
Ah, because I didn't realize 2pi(r) wasn't a constant. 2pi would be k and radius and height would be variables so thinking about it that way, the first choice seems best. – Matt May 9 '11 at 15:41
I would go with the first choice as well. – El'endia Starman May 9 '11 at 16:37