A spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 25 cm to 16 cm in 30 minutes. At what rate, in cm3 per minute, is the volume of the snowball changing at the instant the radius is 9 cm?

Explanation:

Given:

initial radius of the snowball,

final radius of the snowball,

time taken for the change,

Now the rate of the change in radius of the snowball:

................(1)

As we know that the volume of sphere:

Now differentiating Volume equation:

...........................(2)

Now when the radius of the sphere is 9 cm:

is the rate of change of volume when the radius is 9 cm.

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