We will find the rate of change of volume with respect to the change of radius.
Volume, V(r) = (4/3) π r^3
Find rate of change of volume with respect to change of radius by differentiation
V'(r)=dV/dr = d[(4/3) π r^3]/dr = (4/3) π d[r^3]/dr =(4/3) π 3r^2
Therefore when diameter=10mm, r=5mm
V'(r)=V'(5)=(4/3) π (3(5^2))=(4/3) π 75 = 100 π mm^3/mm
