Find the largest area of the largest rectangle that can be cut from a circular quadrant of diameter 8 feet.

Question

Can you please help me answer my h.w, your help is greatly appreciated. Please include the solution on how you arrived with the answer. Thank you!

Answer 1

I think all you need is to understand that the circular quadrant in the first quadrant of the plane has equation y = sqrt(4-x²).

Then the area A of the rectangle is x*sqrt(4-x²).

The maximum (if one exists) will be found when dA/dx = 0.

Use the product rule to find the derivative; then set the derivative = 0 and solve for x.

I got x = sqrt(2) which makes the rectangle a square (as I expected!!!).