My calculus test

[Kirby]

Suppose air is pumped into a spherical balloon at the rate of 1/3 ft^3/min. Determine the rate at which the balloon's radius is increasing when the radius is 1/2 foot long.

V = (4/3)*pi*r^3

Anyone here man enough to handle it?

 

[txrandom]

If I remember, I haven't had Calculus I since last semester. I think you take the deritave with respect to time. So dV= 4*pi*r^2*dR, so you plug in. 1/3 = 4*Pi*(1/4)*dr/dt. So dV=1/(3*pi).

Edit- I thought you were finding rate of volume change instead of rate of radius change.

 

[hdeck]

what does being manly have to do with solving a calculus problem for you? lol

 

[JujuFish]

You want to find dr/dt. You're given dv/dt. You need to relate dr/dt to dV/dt and you'll have you're answer.
In this case:
dV/dt = 1/3ft^3/min
V=(4/3)pr^3
dV/dt = 4pr^2*dr/dt
Now, substitute:
1/3ft^3/min=4p(.5)^2*dr/dt

Now, just solve for dr/dt.

 

[Kirby]

Originally posted by: JujuFish
You want to find dr/dt. You're given dv/dt. You need to relate dr/dt to dV/dt and you'll have you're answer.
In this case:
dV/dt = 1/3ft^3/min
V=(4/3)pr^3
dV/dt = 4pr^2*dr/dt
Now, substitute:
1/3ft^3/min=4p(.5)^2*dr/dt

Now, just solve for dr/dt.

ahh, in that case i may have got it somewhat right. maybe i'll get some partial credit. it was a 15pt question on a 70pt test, and i think i got the other questions right. me making a b, ftw!

 

[txrandom]

Is this a college or high school test?