Circles Chapter 8

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.

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

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

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

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= 1 2 16 𝑟= 16 2 𝑟=8 yds 𝑟= 1 2 𝑑 𝑟= 1 2 23 𝑟= 23 2 𝑟=11.5 cm 𝑑=2𝑟 𝑑=2 5.2 𝑑=10.4 units

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

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

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.

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.

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

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

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

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

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

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.

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.

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

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

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

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.

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