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vovikov84 [41]
3 years ago
9

Show that the maximum rate of change, with respect to radius, of the volume of a deflating balloon is four times the sphere's in

itial great circle circumference
Mathematics
1 answer:
dmitriy555 [2]3 years ago
7 0

Step-by-step explanation:

Let's say R is the initial radius of the sphere, and r is the radius at time t.

The volume of the sphere at time t is:

V = 4/3 π r³

Taking derivative with respect to radius:

dV/dr = 4π r²

This is a maximum when r is a maximum, which is when r = R.

(dV/dr)max = 4π R²

This is 4 times the sphere's initial great circle area, but not the great circle circumference.  The problem statement contains an error.

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