How can you find the circumference of a circle if you only know the area?

For Example

A circle has an area 16πcm2. What is the circumference of the circle?

In this lesson you will learn how to find the circumference

of a circle by using the measure of area.

Let’s ReviewLet’s Review

Area of a Circle = πr2

Circumference of a Circle= πd or 2πr

Let’s ReviewLet’s Review

The reverse of squaring a number is finding the square root.

32 = 9

= 3

Let’s ReviewA Common Mistake

Finding the square root of a number is not the same as dividing it by 2.

Wrong

= 8

Correct

= 4

Let’s ReviewCore Lesson

Bill has a circular garden that he wants to put a fence around. He knows that the area of a garden is 16π

yds2. How much fencing does Bill need to go around the circumference of the garden?

A = 16π yds2

A = πr2 C = 2πr

r2 = 16 yds2

r = 4 yds

4 yds C = 2π(4 yds)

C = 8π yds

Let’s ReviewCore Lesson

A circle has an approximate area of 28.26 ft2. If 3.14 was used for pi, what is the circumference of the circle?

A = πr2

28.26 ft2 = 3.14r2

3.14 3.14

9 ft2 = r2

3 ft = r

C = 2πr

C = 2(3.14)3

C = 18.84 ft

In this lesson you have learned how to find the circumference

of a circle by using the measure of the area.

Let’s ReviewGuided Practice

A circle has an area of 25π cm2. What is the circumference of the circle?

Let’s ReviewExtension Activities

The area of a circle is 16π meters2. Stephanie concluded that the circumference of the circle would be 16π. She stated “the radius would be 8 meters since the square root of 16 is 8.” What mistake did Stephanie make. Write an explanation describing how to fix her mistake.

Let’s ReviewExtension Activities

A circle inside of a square touches the square at each edge as shown below. If the circle has an area of 25π feet2, find the area of the square.

Let’s ReviewQuick Quiz

Find the circumference of the circle that has an area of 81π m2.

A circle has an area of 113.04 cm2. What is the circumference of the circle?