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 = (.61.2)/(52) = .2