# Thread: rectangle cut from circle - maxima problem

1. ## rectangle cut from circle - maxima problem

A rectangle is cut from a circular disc of radius 6 cm. Find the area of the largest rectangle that can be produced

2. Originally Posted by differentiate
A rectangle is cut from a circular disc of radius 6 cm. Find the area of the largest rectangle that can be produced
The diagonal of the rectangle is the diameter of the circle.

Let $x$ be the width, $y$ the height.

You want to maximize the function $xy$ given that $\sqrt{x^2+y^2}=12\implies x^2+y^2=144$.

3. Thanks. I got the answer. its 72

4. That looks right. Notice that it's a square. This will often be the case when you want to maximize area (or volume).