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Math Help - word problem

  1. #1
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    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 = \frac{4}{3}{\pi}r^3. Find the rate at which that volume of the balloon is increasing when the diameter is 2 m.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by extraordinarymachine View Post
    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 ...
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  3. #3
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    i forgot to mention i have to use the limit formula to solve
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by extraordinarymachine View Post
    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.....
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  5. #5
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    Quote Originally Posted by extraordinarymachine View Post
    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?)
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    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.
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  7. #7
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    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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