CK-12 Geometry-Concepts

10.10. Area of a Circle http://www.ck12.org

A=π 52 = 25 πcm

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52504

CK-12 Foundation: Chapter10AreaofaCircleB

Concept Problem Revisited

A circle with a radius of 5 inches has areaπ 52 = 25 πin^2.

Vocabulary

Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradiusis
the distance from the center to the outer rim of the circle. Achordis a line segment whose endpoints are on a circle.
Adiameteris a chord that passes through the center of the circle. The length of a diameter is two times the length
of a radius.Areais the amount of space inside a figure and is measured in square units.π, or“pi”is the ratio of the
circumference of a circle to its diameter.

Guided Practice

1. Find the area of the shaded region from Example C.


2. Find the diameter of a circle with area 36π.


3. Find the area of a circle with diameter 20 inches.

Answers:

1. The area of the shaded region would be the area of the square minus the area of the circle.

A= 102 − 25 π= 100 − 25 π≈ 21. 46 cm^2

2. First, use the formula for the area of a circle to solve for the radius of the circle.

A=πr^2

36 π=πr^2

36 =r^2

r= 6

If the radius is 6 units, then the diameter is 12 units.

3. If the diameter is 20 inches that means that the radius is 10 inches. Now we can use the formula for the area of a
   circle.A=π( 10 )^2 = 100 πin^2.