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# Application of Derivatives and Differentiation : Rate of Change of Volume of a Sphere ( Balloon )

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Air is being pumped into a spherical balloon so that the radius is increasing at the rate of dr/dt = 3 inches per second. What is the rate of change of the volume of the balloon in cubic inches per second, when r = 8 inches? Hint: V = 4/3(pi)r^3

https://brainmass.com/math/derivatives/application-of-derivatives-and-differentiation-rate-of-change-of-volume-of-a-sphere-balloon-52737

#### Solution Preview

We have,

Volume of the spherical balloon as, V = (4/3) pi r^3

Now, differentiating it w.r.t time t, we get,

dV/dt = (4/3) pi *( 3 r^2) * dr/dt ( ...

#### Solution Summary

Rate of Change of Volume of a Sphere ( Balloon ) is calculated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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