Homework Help: Math

Posted by melinda on Sunday, January 15, 2012 at 12:45pm.

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 - Reiny, Sunday, January 15, 2012 at 4:36pm
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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