This is just a tutorial on how to solve a problem like this.
The problem is:
So right off the bat I know the following.A Spherical balloon is to be deflated so that its radius decreases at a constant rate of 10 cm/min. At what rate must air be removed when the radius is 8 cm?
Air must be removed at ________ cm^3/min
It's only annoying because I can't find a video tutorial on it.
Equation:
I bring it into it's derivative form.
(just so you know the threes cancel)
Given:
(note: Any one reading this and wondering why it's negative ten is because it is deflating)
My attempt:
Just punch that into a caculator and you'll get the answer of:
This basically will work for any problem that's like this it's just a matter of changing the numbers.
Well I would like the record to show that this problem is in fact right.
My evidence:
Calculus: related rates, spherical balloon, formula for the volume of a sphere
So this one is for archives.
Just one question on theory:
Why doesn't turn out to be 0 or at least something else?