1. Circles
Chapter 8

2. Circumference
A circle is the set of all points in a plane that are the same distance from a point, called the center.
The circumference is the distance around a circle.
The diameter is the distance across a circle through its center.
The radius is the distance from the center to any point on the circle.
Now take your circle and fold it in half 2 ways.

3. Radius and diameter The diameter d of a circle is twice its radius r.
The radius r of a circle is half of its diameter d.
Diameter Radius
Equations: 𝑑=2𝑟 𝑟= 𝑑 2

4. Example 1 The diameter of a circle is 14 inches. Find the radius.
𝑟= 1 2 𝑑 𝑟=
r = 7 inches

5. Example 2 The radius of a circle is 8 feet. Find the diameter. 𝑑=2𝑟
𝑑=2 8
𝑑=16 feet

6. You try
Find the radius or diameter of each circle with the given dimensions.
a. d = 23 cm b. r = 3 in. c. d = 16 yds. d. r = 5.2
𝑑=2𝑟
𝑑=2 3
𝑑=6 in.
𝑟= 1 2 𝑑 𝑟=
𝑟= 16 2
𝑟=8 yds
𝑟= 1 2 𝑑 𝑟=
𝑟= 23 2
𝑟=11.5 cm
𝑑=2𝑟
𝑑=2 5.2
𝑑=10.4 units

7. Circumference
The circumference of a circle is equal to 𝜋 times its diameter or 𝜋 times twice its radius.
Equation:
Given diameter: 𝐶=𝜋𝑑
Given radius: 𝐶=2𝜋𝑟

8. Example 3
Find the circumference of a circle with a radius of 21 inches.
𝐶=2𝜋𝑟
𝐶=2𝜋(21)
𝐶=42𝜋 inches

9. On your own Find the circumference of each circle. 𝐶=2𝜋𝑟 𝐶=2𝜋 7 8
𝐶=2𝜋 7 8
𝐶=𝜋 7 4
𝐶= 7 4 𝜋 ft.
𝐶=𝑑𝜋
𝐶=70𝜋 in.

10. 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.
𝐶=𝑑𝜋
𝐶=23𝜋 ft.
Multiply 23 by 3.14 to get an estimate.
𝐶≈72.22 𝑓𝑡.

11. Homework
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12. Bellwork: 4/23 Find the circumference of the following circles. 42 cm
112 mm

13. Area of a Circle
The area of a circle equals the product of 𝜋 and the square of its radius.
𝐴=𝜋 𝑟 2

14. Example 1
Find the area of the circle. Use 3.14 for π
2 in.

15. Example 2
Find the area of a circle with a radius of 14 centimeters. Use 3.14 for π

16. On your own
Find the area of a circle with a radius of 3.2 feet. Use 3.14 for π

17. Example 3
Find the area of the face of the Virginia quarter with a diameter of 24 millimeters. Use 3.14 for π. Round to the nearest tenth if necessary.

18. On your own
Find the area of the face of the Virginia quarter with a diameter of 24 millimeters. Use 3.14 for π. Round to the nearest tenth if necessary.

19. Area of Semicircles 𝐴= 1 2 𝜋 𝑟 2
A semicircle is half of a circle. The formula for the area of a semicircle is
𝐴= 1 2 𝜋 𝑟 2

20. Example 4
Find the area of the semicircle. Use 3.14 for π. Round to the nearest tenth.
16 in.

21. On your own
Find the approximate area of a semicircle with a radius of 6 centimeters.

22. Example 5
On the basketball court there is a semicircle above the free-throw line that has a radius of 6 feet. Find the area of the semicircle. Use 3.14 for π. Round to the nearest tenth.

23. Homework
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