The radius of a sphere is increasing at a rate of 0.50., point, 5 centimeters per minute. At a certain instant, the radius is 17 centimeters. What is the rate of change of the volume of the sphere at that instant (in cubic centimeters per minute)

dV/dt  = 1814,92 cm³/min

Step-by-step explanation:

Volume of the sphere is :

V(s)  =  (4/3)*π*x³    (1)        x is radius of the sphere

Differentiating in relation to time of equation (1)

dV/dt  =(4/3)*π*3*x²*dx/dt

Now we know dx/dt  = 0, 5 cm/min

And we have to  find  dV/dt   when  radius is 17 cm

dV/dt  = 4*π*x²*0,5

dV/dt  = 12,56*(17)²*0,5

dV/dt  = 12,56*289*0,5

dV/dt  = 1814,92 cm³/min

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~coco