Bobosharif S. answered • 03/18/18

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First, the Volume of the sphere is calculated by V=(4/3)πr

^{3}, and d=2r, therefore V=(1/6)πd^{3}. Since V is increasing with time, this means that V =V(t), (d=d(t) as well) and we have to look for the change of V over time, i.e, derivative of V(t) w.r. to time;dV/dt=(1/2)πd

^{2}d(d)/dtd(d)/dt=2(dV/dt)/(πd

^{2})=2*10/(20^{2}π)=1/(20π).that is the reate of increases of diameter is 1/(20π)cm/second.

TH