Find the area of the largest rectangle that fits inside a circle of radius 4.

Question

Applications and derivative questions

Answer 1

Radius of the circle r = 4.

Length of the rectangle = l

Width of the rectangle = w

From the above figure and using Pythagorean theorem

Area of the rectangle A = lw

To obtain the the largest rectangle that fits inside a circle,apply derivative both sides with respect to l.

Area is always constant.So Derivative of area is equals to zero.

Substitute value of l in w formula

The largest rectangle area that fits inside a circle is

Solution : The largest rectangle area that fits inside a circle with radius 4 is 8 square units.