Volume of circular cylinder

Question

If the volume of the circular cylinder is given with the 𝑽=𝝅𝒓𝟐𝒉 and 𝟕𝒓=𝟓𝒉, if the height increases by 0.02 m/sec, Find the rate of increase in the volume of the cylinder when 𝒉=𝟏𝟒𝒄𝒎

Answer 1

V = pir^2h

7r = 5h

r =5h/7

V = pi(5h/7)^2(h)

= 25pi/49)(h^3)

take the derivative of V evaluated when h'=.02 and h=14

V' = (3)(25pi/49)h^2(h')

V' = (75pi/49)(14)^2(.02) = rate of change in Volume