# Surface integral

1. Oct 15, 2008

### delefemiaoa

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution
No idea of solution

2. Oct 15, 2008

### 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.

3. Oct 16, 2008

### delefemiaoa

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

4. Oct 16, 2008

### HallsofIvy

Staff Emeritus
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.

5. Oct 16, 2008

### delefemiaoa

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