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

For Example

A circle has a circumference of 37.68 cm. What is the area of the circle?

In this lesson you will learn how to find the area of a circle by

using the measure of the circumference.

Let’s ReviewLet’s Review

Area of a Circle = πr2

Circumference of a Circle= πd or 2πr

Let’s ReviewA Common Mistake

Divide the diameter by 2 to find the radius.

Find the area of a circle with a diameter of 6 cm.

Wrong

A = π(6cm)2

A = 36πcm2

Correct

A = π(3cm)2

A = 9πcm2

Let’s ReviewCore Lesson

A playground in the shape of a circle has a circumference of 18π yards. What is the area of the

playground?

C = 18π yds.

C = πd

D = 18 yds

18 yds

Let’s ReviewCore Lesson

Area = π(9 yds)2

Diameter = 18 yards

Radius = 9 yards

Area = 81π yds2

18 yds

9 yds

Let’s ReviewCore Lesson

A circle has an approximate circumference of 37.68 cm. If 3.14 was used for pi, what is the area of the circle?

C = πd37.68cm =

3.14d37.68cm = 3.14d

3.14 3.14 d = 12 cm

Let’s ReviewCore Lesson

d = 12 cm

r = 6 cm

A = 3.14(6cm)2

A = 3.14(36cm2)A = 113.04 cm2

A circle has an approximate circumference of 37.68 cm. If 3.14 was used for pi, what is the area of the circle?

In this lesson you have learned how to find the area of a circle by

using the measure of the circumference.

Let’s ReviewGuided Practice

The circumference of a circle is 10π. What is the area of the circle?

Let’s ReviewExtension Activities

The circumference of the Earth is approximately 25,000 miles. If you were to dig a hole to the center of the Earth, how long would the tunnel be? Explain how you found your answer.

Let’s ReviewExtension Activities

The Redwood trees in California are said to have trunks so large that a car could fit in them. Estimate the circumference of the Redwood tree. Use your estimate to then find the area of the trunk if the tree was cut down. Explain your reasoning.

Let’s ReviewQuick Quiz

The circumference of a circle is 12.56 ft². If 3.14 was used to approximate pi, what is the area of the circle?

A circle has a circumference of 9π meters. Find the area of the circle.