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Circles

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

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Circles

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  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 thecircumference of a circle to its diameter. For any circle,if you divide its circumference by its diameter, you get avalue close to 3.14159. This relationship is expressed in thefollowing 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 itscircumference? (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 itscircumference? (Use = 3.14)

  8. Example : The circumference of a circle is 15.7 cm. What isits 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. 16 cm 10.00 cm 28.00 cm 45.00 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 9 in 10 ft

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