1. Circles

2. A circle is a shape with all points the same distance from its center. The distance around a circle is called its circumference. The distance across a circle through its center is called its diameter.

3. (pi) is the ratio of the circumference of a circle to its diameter. For any circle, if you divide its circumference by its diameter, you get a value close to 3.14159. This relationship is expressed in the following formula: C/D = where C is the circumference and D is the diameter.

4. The radius of a circle is the distance from the center of a circle to a point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. So a circle's diameter is twice as long as its radius.

5. The formula for the circumference of a circle is given by either :

6. Example : The diameter of a circle is 3 cm. What is its circumference? (Use = 3.14) Solution: C = d C = 3.14 · (3 cm) C = 9.42 cm 3 cm

7. Example : The radius of a circle is 2 in. What is its circumference? (Use = 3.14)

8. Example : The circumference of a circle is 15.7 cm. What is its diameter? (Use = 3.14) C = d 15.7 cm = 3.14 · d d = 15.7 cm ÷ 3.14 d = 5 cm

9. The area of a circle is the number of square units inside that circle. If each square in the circle below has an area of 1 sq.cm, you could count the total number of squares to get the area of this circle. If there were a total of 28.26 squares, the area of this circle would be 28.26 csq.m

10. The area of a circle is given by the formula

11. Example : The radius of a circle is 3 in. What is its area? (Use = 3.14) Solution: A = · r · r A = 3.14 · (3 in) · (3 in) A = 3.14 · (9 sq.in) A = 28.26 sq.in

12. Example: The diameter of a circle is 8 cm. What is its area? (Use = 3.14) r = 4 cm A = · r · r A = 3.14 · (4 cm) · (4 cm) A = 50.24 sq.cm

13. Example: The area of a circle is 78.5 sq.m. What is its radius? (Use = 3.14) Solution: A = 78.5 sq.m = 3.14 · 78.5 sq.m ÷ 3.14 = 25 sq.m = r = 5 m

14. Find the area of the rectangular piece of metal after the 2 circles are removed. 28.00 cm 45.00 cm 10.00 cm 16 cm

15. Find the perimeter and area of the shape.

16. A belt connecting two 9-in-diameter drums on a conveyor system needs replacing. How many in long must the belt be if the centers of the drums are 10 ft apart? Round to tenths. 9 in 10 ft