The Surface area of a
spherical ball increase at
rate of 30cm^²/s- Find
The rate which volume
is increasing when it is 288πcm².

The rate of change of volume is .

Step-by-step explanation:

The surface area of the sphere of radius is given by

.

and the volume of the same is

Now we are told that there rate of change of surface area is or

which means

From the product rule we see that

which we substitute into equation (3) to get:

Now, we find the rate of change of volume by taking the time derivative of equation (2) as follows:

From the product rule

and since

,

we have

putting this into equation (5) we get:

from equation (4) we substitute the value of to get:

Now, when the area is , the radius is

,

putting that into equation (7) we get

Thus, the rate of change of volume is

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step-by-step explanation:

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