Circles

Warm Up Find the area of each figure. 11.25 𝑐𝑚 2 408 𝑐𝑚 2 1). 39 cm 11.25 𝑐𝑚 2 408 𝑐𝑚 2 1). 39 cm 2). 4.5 cm 34 cm 24 cm 5 cm 2.4 yd. 4 in 3). 4). 5.5 in 3 yd. 5.67 yd. 12 in 44 𝑖𝑛 2 12.105 𝑦𝑑 2

Circles Diameter Radius Radius- a line segment whose endpoints are the center of a circle and any point on the circle. Diameter- a line segment that passes through the center of a circle and whose endpoints lie on the circle.

Circumference Circumference is the distance around a circle. The circumference is about three times the length of the diameter.

Circumference Relationships If the circumference of the circle is 24 inches what is the approximate diameter? The diameter is about 8 inches.

Circumference Relationships If the circumference of the circle is 36 inches what is the approximate radius? The radius is about 6 inches.

Circumference Relationships What is the relationship between the circumference and diameter of any circle? The circumference is about 3 times (pi) the length of the diameter.

Circumference Relationships What is the relationship between the circumference and radius of any circle? The circumference is about 6 times the length of the radius.

Practice Give the approximate radius and diameter of each circle for the given circumference. 1). 2). 3). 4). 16 in Diameter is about 5 inches the radius is about 2.5 inches 50 ft. The diameter is about 16 feet and the radius is about 8 feet 100 cm The diameter is 33 cm and the radius is about 17 cm 30 m The diameter is about 10 meters and the radius is about 5 meters.

Circumference

Flippable

𝐂𝐢𝐫𝐜𝐮𝐦𝐟𝐞𝐫𝐞𝐧𝐜𝐞= 𝛑𝐝 Circumference Circumference is the distance around a circle. The circumference is about 3 times the diameter or the diameter times 3.14 (𝝅). 𝐂𝐢𝐫𝐜𝐮𝐦𝐟𝐞𝐫𝐞𝐧𝐜𝐞= 𝛑𝐝

𝝅 is 3.14 3.14 x 13 = 40.82 in Example 1: Find the circumference. Diameter is 13 in 𝝅 is 3.14 13 in 3.14 x 13 = 40.82 in

3.14 x 11 = 34.54 cm Example 2: Find the circumference. Radius is 5.5 cm so the Diameter is 11 cm 5.5 cm 3.14 x 11 = 34.54 cm

Practice Find the circumference of each circle. 1). 2). 3). 4). 5 in 31.4 in 15 in 47.1 in 12 in 75.36 in 23 in 72.22 in

Area of Circles

Warm Up Find the circumference of each circle. 1). 2). 3). 4). 31.4 in 1). 2). 3). 4). 31.4 in 3 ft. 9.42 ft. 5 in 43.96 yd. 81.64 cm 26 cm 7 yd.

Flippable

Area Area of a circle is found by multiplying pi(3.14) and the radius squared (radius x radius). 𝐴=𝜋 𝑟 2

𝑨=𝝅 𝒓 𝟐 Example 1: Multiply the radius times the radius 8 x 8 = 64 8 in Multiply 64 and 3.14 (pi). The answer is 200.96 𝒊𝒏 𝟐 .

𝑨=𝝅 𝒓 𝟐 Example 2: 13 cm Next, square the radius. 𝟔.𝟓 𝟐 =𝟒𝟐.𝟐𝟓 The first thing you need to do is find the radius. The diameter is 13. The radius is half of the diameter so the radius is 6.5 (𝟏𝟑÷𝟐). 13 cm Next, square the radius. 𝟔.𝟓 𝟐 =𝟒𝟐.𝟐𝟓 Multiply 42.25 and 3.14 (pi). Your answer is 132.665 𝒄𝒎 𝟐 .

78.5 𝒊𝒏 𝟐 176.625 𝒊𝒏 𝟐 452.16 𝒊𝒏 𝟐 415.265 𝒊𝒏 𝟐

The Area and Perimeter of a Circle A circle is defined by its diameter or radius radius The perimeter or circumference of a circle is the distance around the outside The area of a circle is the space inside it Diameter The ratio of π (pi) π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14 The circumference is found using the formula C=π d or C= 2πr (since d=2r) The area is found using the formula C=πr2

Closure Solve the following problem. The circumference of Jon’s bike wheel is 7.85 feet. What is the diameter of his wheel? 2.5 ft.

Closure Solve the following problem. The circumference of Jon’s table is 18.84 feet. What is the area of the table? 28.26 𝒇𝒕 𝟐