Q. 28 - Calculus

Question

Use optimization techniques to answer the questions in Exercises 25–30.
Find the area of the largest rectangle that fits inside a circle of radius $4$.

Step-by-Step Solution

Answer

The area of the rectangle is $32$.

Step 1. Given Information.

Radius of circle is $4$.

Step 2. Form an equation.

Let x be the length of the given rectangle.

From the given information, 

Diameter$,=4\times 2$

                 $=8$

Step 3. Use Pythagoras theorem to find x.

Using Pythagoras theorem,

$$\begin{gathered} x^2+x^2=8^2 \\ 2x^2=64 \\ x^2=32 \end{gathered}$$

Step 4. Find the area of rectangle.

The area of the rectangle which fits inside the area of the circle is the area of the square.

$x^2=32$