Worded calculus question: how fast is radius increasing?

[Sooty]

Air is being pumped into a spherical ballon so that its volume increases at a rate of 80pi cm^3/s/ How fast is the radius, r, increasing when r=2? (you may find it useful to know the volume of a sphere of radius r is given by V=4/3 pi r^3)

I've been running a mock trying to figure this question out for ages (2 hours). I've got an exam tomorrow and I seriosuly don't think I know how to figure out this worded calculus questions!!

If anyone could help it would be fantastic!

 

[galactus]

You want \(\displaystyle \L\\\frac{dr}{dt}\) given that \(\displaystyle \L\\\frac{dV}{dt}=80{\pi}\)

\(\displaystyle \L\\V=\frac{4}{3}{\pi}r^{3}\)

\(\displaystyle \L\\\frac{dV}{dt}=4{\pi}r^{2}\frac{dr}{dt}\)

Enter in your given data and solve for \(\displaystyle \L\\\frac{dr}{dt}\)

 

[Sooty]

thanks figured that out!

i'll take a look at some other peoples probs and help them once my exam is over!

in the mean time just trying to get my head around rate of change calculus questions...

2. "A spectator standing at a distance of 3000m from a lauch site, is observing a rocket launch. The rocket is launched vertically and is rising at a rate of 300m/sec.
When its altitude is 4,000m how fast is the distance between the rocket and the spectator changing at that instant?"[/i]


2. dd/dt = 300m/s


argh... i can find small bits from the worded equations but not the whole thing. its really annoying!!!

 

[galactus]

Start a new thread when posting another problem. Folks stand a better chance of seeing it.

Find \(\displaystyle \frac{dy}{dt}\) given that \(\displaystyle \frac{dx}{dt}=300\)

\(\displaystyle y^{2}=x^{2}+3000^{2}\)

\(\displaystyle 2y\frac{dy}{dt}=2x\frac{dx}{dt}\)

\(\displaystyle \frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}\)


If x=4000, then y=5000

Enter in your data and solve.