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The volume of a sphere is decreasing at a constant rate of 2032 cubic inches per minute. At the instant when the volume of the sphere is 342342 cubic inches, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=\frac{4}{3}\pi r^3.V=
3
4
​
πr
3
. Round your answer to three decimal places.

Respuesta :

rspill6

Answer: 0.1"/minute

Step-by-step explanation:

Volume of a sphere is:  V = (4/3)πr³

In one minute, the volume increases by 2032 in^3.  Set the starting volume at a point 1 minute from the target of 342342 in^3:  (342342 - 2032) =  340310 in^3.

We can then determine the change in the radius for the initial (340310 In^3) and end (342342 in^3) points as the sphere reaches its maximum size:

Initial:  The radius for a 340310 in^3 sphere is 43.3".

Finish:  The radius for a 342342 in^3 sphere is 43.4".  {Wow]

It took an increase in radius of 0.1" to add the final 2032 in^3 of volume to the sphere.  That occurred in one minute, so the rate of change of the radius is 0.1"/minute.

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