- #1

Elias Waranoi

- 45

- 2

## Homework Statement

Inscribe in a given cone, the height h of which is equal to the radius r of the base, a cylinder (c) whose total area is a maximum. Radius of cylinder is r

_{c}and height of cylinder is h

_{c}.

## Homework Equations

A = 2πr

_{c}h

_{c}+ 2πr

_{c}

^{2}

## The Attempt at a Solution

r = h ∴ h

_{c}= r - r

_{c}

A = 2πr

_{c}(r - r

_{c}) + 2πr

_{c}

^{2}

To get the maximum of this area I will find the radius r

_{c}when the growth of the area is zero.

dA/dr

_{c}= 0 = 2πr

What does this result mean? I don't understand how 0 = 2πr makes sense as a result from a derivation. What kind of information does this result give me geometrically? How can I know that there is no maximum area to the cylinder as my answer sheet tells me.