Help! Related Rates
- Thread starter Bma
- Start date
Hello, and welcome to FMH!
What is the volume \(V\) of a sphere, in terms of its radius \(r\)?
I don't know. It is not shown from the question.
I haven't done it yet because I don't know how to do it, that's why I'm asking for help here.
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- Nov 24, 2012
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What I'm asking you to do is to complete:
[MATH]\frac{d}{dt}\left(V\right)=\frac{d}{dt}\left(\frac{4}{3}\pi r^3\right)[/MATH]
When we perform the indicated differentiations, we obtain:
[MATH]\d{V}{t}=4\pi r^2\d{r}{t}[/MATH]
Now, on the LHS we have the time rate of change of the volume (which is what we're being asked to find) and on the right we just need to plug in the given data:
[MATH]r=30\text{ cm}[/MATH]
[MATH]\d{r}{t}=5\frac{\text{cm}}{\text{s}}[/MATH]
So, putting those in, what do you conclude?
[MATH]\frac{d}{dt}\left(V\right)=\frac{d}{dt}\left(\frac{4}{3}\pi r^3\right)[/MATH]
When we perform the indicated differentiations, we obtain:
[MATH]\d{V}{t}=4\pi r^2\d{r}{t}[/MATH]
Now, on the LHS we have the time rate of change of the volume (which is what we're being asked to find) and on the right we just need to plug in the given data:
[MATH]r=30\text{ cm}[/MATH]
[MATH]\d{r}{t}=5\frac{\text{cm}}{\text{s}}[/MATH]
So, putting those in, what do you conclude?
Steven G
Elite Member
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- Dec 30, 2014
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I just want to point out something. Asking for help and asking for the answer are not the same thing. MarkFL tried his best to get something out of you but you did not try. At this point in calculus you should know how to compute a derivative.