Answer :

The rate of increase in the volume of sphere when  diameter is 100 mm is 94285.71 mm³/s.

Describe the rate of volume increase?

  • The indicator that demonstrates whether or not the volume trend is emerging either in an up or down direction is the volume rate of change.

Let the radius of the sphere be 'r'.

The radius of a sphere is increasing at a rate of 3 mm/s .

Then,

dr / dt = 3 mm/s

Volume of sphere is given as;

v = 4/3 π r³

Then, the change is volume is;

dv / dt = (4/3)  π 3r² .dr/dt

         = 4πr² x 3

         = 12πr²

For radius = 100/2 mm = 50 mm

dv / dt  = 12 x 22/7 x 50²

dv / dt  = 94285.71 mm³/s

Thus, the rate of increase in the volume of the sphere when diameter is 100 mm is 94285.71 mm³/s.

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