### Home > CCG > Chapter Ch8 > Lesson 8.3.3 > Problem8-128

8-128.

The Isoperimetric Theorem states that of all closed figures on a flat surface with the same perimeter, the circle has the greatest area. Use this fact to answer the questions below.

1. What is the greatest area that can be enclosed by a loop of string that is $24$ cm long?

The $24$ cm loop of string is the circumference of the circle. $2\pi r = 24$.

Once you solve for $r$, substitute it into the equation: area of a circle $= \pi r^2$.

area $\approx 45.84 \text{ cm}^2$

2. What is the greatest area that can be enclosed by a loop of string that is $18\pi$ cm long?

The only difference between the two parts of this problem is that the length of the loop of string has been changed.
Therefore, follow the same steps used in part (a) to find the answer to part (b).