anonymous 3 years ago You're filling a water balloon with a spherical shape. If the water is coming in at 4 cubic inches per second, how fast is the radius changing when the volume is 200 cubic inches? (answer: 0.0241 in/sec)

1. anonymous

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2. anonymous

@sweett2639 do you follow?

3. anonymous

$v= \frac{ 4 }{ 3 } \pi r ^{3}$i understand that the volume of a sphere is and that$\frac{ dv }{ dt } = 4 inches ^{3}/\sec$ but not much more than that

4. anonymous

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5. anonymous

so you set 200 equal to v and moved the equasion around so that r is 3.628

6. anonymous

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7. anonymous

Right, we know that the volume is 200 in^3 at the moment of interest, therefore we can find what the radius of the sphere is at that moment

8. anonymous

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9. anonymous

everytime i try to calculate r, i get the wrong number

10. anonymous

http://www.wolframalpha.com/input/?i=4%2F%284*pi*%283.628%29%5E2%29 just make sure you type it into the calc correctly.