Seventh Grade Geometry Unit 5 Standard CC 7

Seventh Grade Geometry Unit 5

Standard CC. 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.

Essential Questions • How are the diameter and circumference of a circle related? • What is pi? How does it relate to the circumference and diameter of a circle? • How do we find the circumference of a circle?

Circumference – the distance around a circle. Diameter – the distance across a circle making certain to go through the center. Radius – the distance from the edge of a circle to the center.

How are the diameter and circumference of a circle related? It takes 3. 14 diameters of any circle to be equal to the length of its circumference. This is pi. Circumference = π d

Animation

* Find the circumference of each circle below. 37. 68 in Circumference = _________ C = π d C = π 12 in C = 37. 68 in 43. 96 cm Circumference = _________ C = π d C = π 14 cm C = 43. 96 cm

* If a circle has a circumference of 29 π inches, what is the radius of that circle? C = π d C = 29π That means the diameter is 29 in. Therefore, the radius is 14. 5 in.

C = π d C = π 150 ft C = 471 ft

• Trevor needs a new bicycle tire. His tire has a circumference of 113. 04 inches. What is the diameter of the tire? ______ 36 inches C = π d 113. 04 = 3. 14 d 36 = d

1. Cam has a bike with 24 inch wheels (diameter). What is the distance of one revolution of his tire? Hint: One revolution of the tire is the circumference. C = π d C= 3. 14 24 in C= 75. 36 in

1. Cam has a bike with 24 inch wheels (diameter). When he rides from his house to the store, his bike tires complete 50 revolutions. What is the distance IN FEET that he has traveled? Hint: One revolution of the tire is the circumference. C = π d C= 3. 14 24 in C= 75. 36 in This is only one revolution…He completed 50 revolutions… 75. 36 inches 50 = 3768 inches Don’t forget to convert inches to feet. 3768 ÷ 12 = 314 feet.

in 3 2. 3 in Find the circumference of the circle labeled blue. C = π d C= 3. 14 12 in C = 37. 68 in Circumference = _________ 37. 68 in.

Find the circumference of each inner circle and outer circle. 1. 2. 3. Inner circle C = π d C= 3. 14 10 cm C= 31. 4 cm Inner circle C = π d C= 3. 14 9 ft C= 28. 26 ft Inner circle C = π d C= 3. 14 22 m C= 69. 08 m Outer circle C = π d C= 3. 14 20 cm C= 62. 8 cm Outer circle C = π d C= 3. 14 ft C= 43. 96 ft Outer circle C = π d C= 3. 14 44 m C= 138. 16 m

Decorating Sandra bought a round table for her room that has two layers. She thinks the table is too plain and wants to glue ribbon around the edges of the layers. One circle has a diameter of 18 inches. The other has a radius that is one third as big as the diameter of the larger circular top. How much ribbon should she buy? 56. 52 + 37. 68 = 94. 20 inches

Closing What is circumference and how do you find circumference of a circle?