Surface Integral: Calculating Max Area from Circular Log

[delefemiaoa]

Homework Statement

A log of wood which is approximately circular in cross section has diameter equal to 0.5m. Calculate the maximum area of the rectangular timber section that can be obtained from the log.

Homework Equations

The Attempt at a Solution

No idea of solution

 

[Dick]

You have to at least get started. Draw a circle with a rectangle inscribed in it. Label the sides x and y. Can you find a relation between x and y? Use geometry.

 

[delefemiaoa]

I have done that before but I can not deduce any relation between x and y.

 

[HallsofIvy]

Finding that maximum area should be simple if you can assume that the greatest area amoung rectangles is always taken by a square. When you drew the picture, you should have seen a square with diagonal length equal to the diameter of the log. You can use the Pythagorean theorem to determine the relation between the sides of that square and its diagonal length.

But since this is posted under "Calculus" I presume you are intended to show that by differentiating a formula. And, if you are taking Calculus, I suspect you are assumed to know the formula for a circle of radius R with center at (0,0). If you don't know it, you should try to look it up.

 

[delefemiaoa]

Thanks a lot, I can now understand how to solve it.