This document provides instruction on calculating properties of circles. It defines key terms like circumference, diameter, radius and pi. It gives the formulas for calculating diameter from radius, radius from diameter, and circumference from diameter or radius using pi. Examples are provided to demonstrate calculating diameter from radius, radius from diameter, and circumference from radius. The final examples ask students to use what they learned to find the diameter and circumference of a circle with a given radius.

1. Identify each solid. Name the number and shapes of the faces. Then
name the number of edges and vertices.
1.
2.
Course 2, Lesson 8-1

2. ANSWERS
1. cube; 6 faces, all squares; 12 edges; 8 vertices
2. rectangular prism; 6 faces, all rectangles; 12 edges;
8 vertices
Course 2, Lesson 8-1

3. HOW do measurements help you
describe real-world objects?
Geometry
Course 2, Lesson 8-1

4. Course 2, Lesson 8-1 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
• 7.G.4
Know the formulas for the area and circumference of a circle and
use them to solve problems; give an informal derivation of the
relationship between the circumference and area of a circle.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
6 Attend to precision.
8 Look for and express regularity in repeated reasoning.

5. • To find the diameter and
radius of a circle
• To find the circumference of
a circle
Course 2, Lesson 8-1
Geometry

6. Course 2, Lesson 8-1
Geometry
• circle
• center
• circumference
• diameter
• radius
• pi (π)

7. Course 2, Lesson 8-1
Geometry
Words The diameter d of a circle is twice its radius r. The radius r
of a circle is half of its diameter d.
Symbols d = 2r r =
2
d

8. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. The diameter of a circle is 14 inches. Find the radius.
Radius of circle
Replace d with 14.
r =
r =
r = 7
The radius is 7 inches.
Divide.

9. Answer
Need Another Example?
The diameter of a circle is 48 centimeters. Find the radius.
24 cm

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. The radius of a circle is 8 feet. Find the diameter.
Diameter of circle
Replace r with 8.
d = 2r
d = 2 • 8
d = 16
The diameter is 16 feet.
Multiply.

11. Answer
Need Another Example?
The radius of a circle is 9 inches. Find the diameter.
18 in.

12. Course 2, Lesson 8-1
Geometry
Words The circumference of a circle Model
is equal to times its diameter
of times twice its radius.
Symbols c = d or C = 2 r




13. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. Find the circumference of a circle with a radius of 21 inches.
Divide by the GCF, 7.
Circumference of a circle
Since 21 is a multiple of 7, use for π.
C = 2πr
C ≈ 2 • • 21
C ≈ 2 • •
Replace π with and r with 21.
3
1
C ≈ 132
The circumference of the circle is about 132 inches.
Simplify.

14. Answer
Need Another Example?
Find the circumference of a circle with a
radius of 35 inches.
about 220 in.

15. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. Big Ben is a famous clock tower in London, England. The
diameter of the clock face is 23 feet. Find the circumference
of the clock face. Round to the nearest tenth.
Multiply.
Circumference of a circle
C ≈ 3.14(23)
C ≈ 72.2
Replace π with 3.14 and d with 23.
So, the distance around the clock is about 72.2 feet.
C = πd

16. Answer
Need Another Example?
John is making a circular table that has a top with a
diameter of 24 inches. Find the circumference of the
table. Round to the nearest tenth.
75.4 in.

17. How did what you learned
today help you answer the
Course 2, Lesson 8-1
Geometry
HOW do measurements help you
describe real-world objects?

18. How did what you learned
today help you answer the
Course 2, Lesson 8-1
Geometry
HOW do measurements help you
describe real-world objects?
Sample answers:
• The diameter is the distance across a circular object,
passing through its center.
• The circumference is the distance around a circular
object.

19. Find the diameter and
circumference of a circle
with a radius of 5 miles
to the nearest tenth.
Course 2, Lesson 8-1
Ratios and Proportional RelationshipsFunctionsGeometry