Ms. Woodman s Mathematics Name: Period:

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1 Ms. Woodman s Mathematics Name: Period: Geometry: Draw, construct, and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Common Core State Standard 7.G.4 Know the formulas for the area and the 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. Circumference: The formula for CIRCUMFERENCE of a circle is: C = π X d (Circumference = Pi times Diameter) Where = The distance around a CIRCLE is called its circumference. The distance across a circle through its center is called its diameter. We use the Greek letter to represent the ratio of the circumference of a circle to the diameter. The diameter of a circle is twice as long as the RADIUS. This relationship is expressed in the following formula: d = 2 x r. Example: What is the circumference of a circle with a radius of 2m? Radius = r = 2 Diameter = r + r Circumference = π d = π d = π (2 + 2) = 3.14 X 4 = m

2 Circumference: CIRCUMFERENCE of a circle is: C = π x d π = 3.14 d = diameter r = radius diameter = r + r or 2r Find the unknown length for each circle: 1. r = 35 mi, d =? 2. d = 6.8 yd, r =? 3. r = 18 ft, d =? 4. d = 0.25 km, r =? 5. A circular jar of jelly beans has a radius of 4 in. What expression describes the circumference of the jar in inches? Worksheet created by Sadhana Woodman

3 Find the circumference of each circle: CIRCUMFERENCE of a circle is: C = π x d 6. C = 7. c = 8. A circular pond has a radius of 10 feet. What is the circumference of the pond? 9. d = 10 m Objects from mathisfun.com and mathgoodies.com

4 10. Writing in math. A pebble is stuck on the tire of your bicycle. As the tire turns, every 68 inches the pebble leaves a mark in the sand. Explain how you would find the circumference of the tire. Radius, Diameter and Circumference

5 Ms. Woodman s Mathematics Name: Period: Circumference LAB CIRCUMFERENCE of a circle is: C = π x d Materials: several circular objects, centimeter rulers, flexible metric tape measure Measure the following objects and record the Circumference of each object: 1. The classroom doorknob 2. The classroom globe

6 Measure and then find the circumference of the objects in your CIRCUMFERENCE LAB box: 3. Can 4. Ball 5. Jar 6. Circular cut-out

7 Patterns: 7. Measure the distance around one of the circular objects. Then measure the distance across the same object. Divide: the distance around the circle (circumference) by the distance across the circle (diameter). C D Object: Explain what your answer means.

8 Ms. Woodman s Mathematics Name: Period: You Can Draw It Yourself Put a tack in the center of this paper, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw a circle. Next: Measure the circumference of the circle: Worksheet created by Sadhana Woodman

9 Ms. Woodman s Mathematics Name: Period: Geometry: Draw, construct, and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Common Core State Standard 7.G.4 Know the formulas for the area and the 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. The area of a circle is the number of square units inside that circle. If each square in the circle to the left has an area of 1 cm 2, you could count the total number of squares to get the area of this circle. Thus, if there were a total of squares, the area of this circle would be cm 2 However, it is easier to use one of the following formulas: where A is the area, and r is the radius. AREA of a CIRCLE or A = π x r x r or A = π x r 2 AREA: Example: What is the area of a circle with radius of 3 m? Radius = r = 3 Area = π r 2 = π 3 2 = π (3 3) = = m 2 ( rounded to 2 decimal places)

10 AREA AREA of a CIRCLE or A = π x r x r or A = π x r 2 A is the area r is the radius. Find the AREA of the following circles: Use 3.14 for π Round answers to the nearest tenth. 1. r = 1.1 m 2. d = 2.4 cm 3. r = 0.5 m 4. d = 13.7 ft 5. Find the AREA of the circle below:

11 6. Find the AREA of the circle below: 7. r = 2 in 8. r = 4 in 9. r = 8 in 10. What happens to the area of a circle if you double the radius? 11. Your class goes on a camping trip. You arrange stones in a circle around the fire pit. The circle has a diameter of 5 feet. Find the area of the fire pit. Round your answer to the tenths place.

12 Drawing in MATH: 12. Find the area of the circle you drew with the tack and string. Writing in MATH: 13. Does a circular cake with a diameter of 20 inches have a greater area than a square pan with a side that is 18 inches long? Worksheet created by Sadhana Woodman

13 Ms. Woodman s Mathematics Name: Period: Area LAB AREA of a CIRCLE or A = π x r x r or A = π x r 2 where A is the area, and r is the radius. Find the AREA of the following objects in centimeters: 1. Circular Tangram 2. Circular Plate 3. Circular Lid 4. Top of a soda can (area of base) 5. Circular cut-out Worksheet created by Sadhana Woodman

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