Precalculus

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How do you setup the equation for this?

Thanky ou!

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.

b) Is the ratio increasing of decreasing? justify answer based on part a.

• Precalculus -

It is not clear if the surface area includes the top and bottom. I will assume not
then
area = 2 pi r h
volume = pi r^2 h
ratio = 2 /r

well that is too easy, try including top and bottom
area = 2 pi r h + 2 pi r^2
volume = pi r^2 h

ratio = 2/r + 2/h
= 2/r + .2 if h = 10

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