CK-12 Geometry Concepts

http://www.ck12.org Chapter 10. Perimeter and Area

Concept Problem Revisited

The entire length of the crust, or the circumference of the pizza is 14π≈ 44 in.

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.Circumferenceis the distance around a circle.π, or“pi”is the ratio of the circumference of a circle to

its diameter.

Guided Practice

1. Find the perimeter of the square. Is it more or less than the circumference of the circle? Why?


2. The tires on a compact car are 18 inches in diameter. How far does the car travel after the tires turn once? How
   far does the car travel after 2500 rotations of the tires?


3. Find the radius of circle with circumference 88 in.
   Answers:


4. The perimeter isP= 4 ( 10 ) = 40 in. In order to compare the perimeter with the circumference we should change
   the circumference into a decimal.

C= 10 π≈ 31. 42 in. This is less than the perimeter of the square, which makes sense because the circle is smaller
than the square.

2. One turn of the tire is the circumference. This would beC= 18 π≈ 56. 55 in. 2500 rotations would be 2500·


3. 55 in≈ 141 , 375 in, 11,781 ft, or 2.23 miles.


4. Use the formula for circumference and solve for the radius.

C= 2 πr

88 = 2 πr

44

π

=r

r≈ 14 in

Practice

Fill in the following table. Leave all answers in terms ofπ.

TABLE10.1:

diameter radius circumference

1. 15


2. 4


3. 6


4. 84 π


5. 9


6. 25 π