# Thread: word problem

1. ## word problem

not too sure how to set this one up, any help would be appreaciated, thanks!

The Happy Face Fix-It shop is having a sales promotion day. A spherical Happy Face balloon is being inflated to float above the shop. The volume, V, of a spherical balloon is V = $\displaystyle \frac{4}{3}{\pi}r^3$. Find the rate at which that volume of the balloon is increasing when the diameter is 2 m.

2. Originally Posted by extraordinarymachine
not too sure how to set this one up, any help would be appreaciated, thanks!

The Happy Face Fix-It shop is having a sales promotion day. A spherical Happy Face balloon is being inflated to float above the shop. The volume, V, of a spherical balloon is V = $\displaystyle \frac{4}{3}{\pi}r^3$. Find the rate at which that volume of the balloon is increasing when the diameter is 2 m.
Differentiate

$\displaystyle V'(r)=4{\pi}r^2$

Now, $\displaystyle D=2\Rightarrow{r}=1$

Then

$\displaystyle V'(1)=4\pi(1)^2=4$ ...

3. i forgot to mention i have to use the limit formula to solve

4. Originally Posted by extraordinarymachine
i forgot to mention i have to use the limit formula to solve
Disregard my last post. I didn't read it correctly.

So.......
One sec.....

5. Originally Posted by extraordinarymachine
i forgot to mention i have to use the limit formula to solve
Then do so. Asking someone else how to do it is NOT "using the limit formula". (What limit formula, by the way?)

6. Originally Posted by HallsofIvy
Then do so. Asking someone else how to do it is NOT "using the limit formula". (What limit formula, by the way?)

i'm not really sure how to explain it, i guess its just using limits. and i know how to use it on my other word problems, but this one is different, and i don't know how to set it up.

7. Do you mean solve using first principles?

given two points:

$\displaystyle P(x,f(x))$

and

$\displaystyle P_{1}(x+h,f(x+h))$

gradient $\displaystyle PP_{1}=\frac{\delta y}{\delta x}=\frac{f(x+h)-f(x)}{(x+h)-x}$

gradient at $\displaystyle P =\lim_{dx\to 0}\frac{\delta y}{\delta x}=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$

$\displaystyle f(x)=\frac{4}{3}\pi r^3$

$\displaystyle f(x+h)=\frac{4}{3}\pi (r+h)^3$

i won't go further.