Math

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How to setup this equation?


Find the ratio of the surface area of a cylinder to the volume of the cylinder if the height remains at 10 cm. Simplify this ratio and let f(x) = the simplified ratio. Let r be the radius of the cylinder.

a) Find the average rate of change as the radius increases from 2 to 5 cm.


Volume:πr^2
SA: 2π^2 + 2πrh

  • Math -

    Both of your formulas are incorrrect

    Vol of cylinger = πr^2 h
    SA = 2πr^2 + 2πrh

    so when h = 10,
    SA/V = (2πr^2 + 20πr)/(10πr^2
    = (r + 10)/(5r)

    f(r) = (r+10)/(5r)
    f(2) = 12/10 = 6/5 = 1.2
    f(5) = 15/25 = .6

    avg rate of change = (.6-1.2)/(5-2) = -.2

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