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The radius of a sphere is decreasing at a constant rate of 6 inches per minute. At the instant when the radius of the sphere is 77 inches, what is the rate of change of the volume? The volume of a sphere can be found with the equation V=\frac{4}{3}\pi r^3.V=34​πr3. Round your answer to three decimal places.

 Feb 20, 2021
 #1
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dV /  dT  =    dV / dr  *  dr / dt

 

dv  / dr  =  4pi r^2

dr / dt  = (-6 in/ min)

 

So

 

dV   / d T  =    4 pi r^2  *  (-6 in /  min)

 

When   r  =  77

 

dV  / dt  =   4pi  (77)^2 *  -6 =    -447036.068  in/ min

 

 

cool cool cool

 Feb 20, 2021

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