Calc I

[Diroga]

the radius of the base of a cylender is increasing at a rate of 2 cm/sec. if the hieght is remais a constant at 100cm find the rate at which the volume of the cylender is increasing when the radius is 20cm

Code:

V = (pi)r^2h

ok so i take the first darivative. but how do i do that? i'm confused wiht how to handle pi. is this right?

Code:

V' = (pi)r^2 dh + 2(pi)rh dr
dh = 0 because it is a constant. dr = 2 cm/sec r = 20 h = 100
V' = (pi)(20)^2(0) + 2(pi)(20)(100)(2 cm/sec)
V' =  8,000(pi) cm^3/sec

[Sterling Christensen]

Looks right to me. It's just the product rule with a constant:

Code:

f(x) = pi * g(x) * h(x)
f'(x) = pi * ( g(x)*h'(x) + g'(x)*h(x) )    (by product rule)
      = pi*g(x)*h'(x) + pi*g'(x)*h(x)       (and then you distributed the pi)

[Diroga]

ok that's what i thought. here is another one i cant get, mostly becae i have no clue what the question is.

An entrepreneur makes and sells moonshine whisky in spherical bottles that cost 60(pi)r^2 cents to make, where r is the radius of the bottle in inches. Suppose the revenue on each cubic inch of whiskey is 15 cents and the largest bottle thta can be made has a radius of 5 inches.

1. shperical bottles are 3 dimetnial, how can it cost 60(pi)r^2 to make?

2. where is the calculus?

Code:

V = (4/3)(pi)r^3 r = 5
V= 500(pi)/3
Cost = 60(pi)r^2 r = 5
Cost = 1500(pi)
Revenue = 500(pi)/3 * 15 -> 2500(pi)
Net Gain = Revenue - Cost -> 2500(pi)-1500(pi) -> 1000(pi) cents -> $34.42

[Sterling Christensen]

That's just two statements and no question. It doesn't say any more than that? Maybe this question is in a group of questions under a heading that tells you what to do with the info in each problem.

1. shperical bottles are 3 dimetnial, how can it cost 60(pi)r^2 to make?

I'm stumped. Could be a typo, but once you find the problem's question you could just run with it, typo and all.

2. where is the calculus?

There isn't any in the quote you gave me, but I think there's more to the problem that you missed. Is there an a., b., etc list under that? Is there an illustration?

If that's all there is to the problem, then you should skip it and show it to your teacher. It just gives you a bunch of info but doesn't tell you what to do with it.

[Diroga]

ah well there is nothing else to the problem. i think you to find the max net gain. i'm not sure that can be done. my teacher said to skip it.