Circumference

Vocabulary

• Center – the point in the middle of the circle

• Circumference – the distance around a circle.

• Diameter – distance across a circle through its center.

• Radius – the distance from the center to any point on the circle.

Hula Hoops

The table shows the approximate measurements

of two sizes of hula hoops.

1. Describe the relationship between the diameter and radius of each hula hoop.

2. Describe the relationship between the circumference and diameter of each hula hoop.

Size Radius Diameter Circumference

Child 14 in. 28 in. 88 in.

Adult 20 in. 40 in. 126 in.

The diameter is twice the radius.

The circumference is about three times the diameter.

Radius and Diameter

• The diameter of a circle, d, is twice its radius.

• The radius, r, of a circle is half of its diameter.

d = 2r

r = 2

d

Radius & Diameter Examples

1. The diameter of a circle is 14 inches. Find the radius.

2. The radius of a circle is 8 feet. Find the diameter.

14 in.2

dr

2

14r

7r

8 ft.

rd 2)8(2d

16d

The radius of the circle is 7 inches.

The diameter of the circle is 16 feet.

Practice Problems

• Find the radius or diameter of each circle with the given dimension.

1. d = 23 cm 2. r = 3 in.

3. d = 16 yd 4. r = 5.2 m

The radius is 11.5 centimeters.

The radius is 8 yards.

The diameter is 6 inches.

The diameter is 10.4 meters.

Circumference • The circumference of a circle is equal to π times

its diameter or π times twice its radius.C = π(d) or C = 2(π)(r)

Example: Find the circumference of a circle with a diameter of 21 inches. Round your answer to the nearest whole number.

C = (π)(d) C = (π)(21)

C = 65.97344573… C = 66 inches

21 in.

The circumference of the circle is 66 inches.

Practice Problems

• Find the circumference of each circle. Round your answers to the nearest tenth.

1. 2. 5 ft. 70 in.

C = 2π(r)

C = 2π(5)

C = 10 π

C = 31.41592654…

C = 31.4 feet

C = π(d)

C = π(70)

C = 219.9114858…

C = 219.9 inches

Word Problem The Belknap shield volcano is located in

the Cascade Range in Oregon. The volcano is circular and has a diameter of 5 miles. What is the circumference of this volcano? Round your answer to the nearest tenth.

C = π(d)

C = π(5)

C = 15.70796327…

C = miles