Patrick D. answered • 04/07/17

Patrick the Math Doctor

V = pi * radius * radius * height = pi * radius^2 * height

pi is approximately 22/7 and height is given to fixed at 5

BUT radius is a function of time, so the chain rule is required.

Moreover, when R=1.5 then dR/dt 0.06 as given in the problem

Substituting, V = 110/7* radius^2 = 110/7*R^2

Differentiating

dV/dt = 220/7 * R * dR/dt

dV/dt = 220/7 * 1.5 * 0.06

= 220/7 * 15/10 * 6/100

= (220*15*6)/(7*10*100)

= (220*90)/(7*10*100)

= (22*9)/70 <-- factor of 100 cancels

= 198/70

= 2 and 58/70

= 2.82857142857142857142857142857....

and that is is cubic centimeters per hour