If you mean average rate of area increase, it is 4pi cm2/cm. Simply take the total change in area, 9pi-1pi=8pi, and divide it by the total expansion.
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Average Transient Rate
i dont know im only 5 A better answer: I assume you are taking differential calculus? A = (pi) R^2 dA/dt = 2 dR/dt cross multiply and find dA/dR = 2 dA/dR = 2 pi R = 2 R = 1/pi
Rate of flow varies as R^4 where R is the radius or Rate of flow = (k) x (R^4)
With the increase in flow rate the velocity of the fluid increases. and with the increase in velocity the pressure decreases, because there will be pressure drop (Refer Bernoulli's Theorm). So with increase in Flow rate the pressure decreases.
They both increase. The rate of increase of the surface area is equivalent to the rate of increase of the volume raised to the power 2/3.