word problem

**extraordinarymachine** · December 8th 2009, 06:50 PM

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 = $\frac{4}{3}{\pi}r^3$ . Find the rate at which that volume of the balloon is increasing when the diameter is 2 m.

**VonNemo19** · December 8th 2009, 07:35 PM

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 = $\frac{4}{3}{\pi}r^3$ . Find the rate at which that volume of the balloon is increasing when the diameter is 2 m.

Differentiate

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

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

Then

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

**extraordinarymachine** · December 8th 2009, 07:38 PM

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

**VonNemo19** · December 8th 2009, 07:42 PM

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.....

**HallsofIvy** · December 9th 2009, 03:55 AM

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?)

**extraordinarymachine** · December 9th 2009, 05:23 AM

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.

**sammy28** · December 9th 2009, 06:27 AM

Do you mean solve using first principles?

given two points:

$P(x,f(x))$

and

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

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

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

substituting your equations:

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

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

i won't go further.

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