Exercise Find the diameter of a circle if

Exercise Find the diameter of a circle if the radius is 5 in. 10 in.

Exercise Find the radius of a circle if the diameter is 5 in. 2. 5 in.

Exercise Find the circumference of a circle if the diameter is 8 cm ≈ 25. 12 cm

Exercise Find the circumference of a circle if the radius is 10 cm. 20 cm ≈ 62. 8 cm

Exercise Find the radius of a circle if the circumference is 31. 4 in. 5 in.

C = 2 r C = d circumference = diameter

Area of a circle A= 2 r The area of a circle (A) is the product of and the square of the radius (r).

Example 1 Find the area of a circle whose radius is 3 km. A = r 2 = (32) = 3. 14(9) ≈ 28. 3 km 2

Example 2 Find the area of a circle whose diameter is 5 m. d 5 r= = = 2. 5 2 2 A = r 2 = (2. 52) = 3. 14(6. 25) ≈ 19. 6 m 2

Example Find the area of a circle with a radius of 5 units. 25 units 2 ≈ 78. 5 units 2

Example Find the area of a circle with a diameter of 12 units. 36 units 2 ≈ 113 units 2

Example Find the radius of a circle if its area is 191 units 2. 7. 8 units

Example Find the area of a circle if its circumference is 62. 8 units. 314 units 2

Example Find the circumference of a circle if its area is 277. 45 units 2. 59 units

Example 3 Find the area of the colored region. A = R 2 − r 2 6 m = (62) − (42) 4 m = 36 − 16 = (36 − 16) = 20(3. 14) ≈ 62. 8 m 2

Example 4 Find the area of the figure. 1 2 A = bh + 2 r = 6. 5(4. 4) + 0. 5(3. 14)(2. 22) = 28. 6 + 0. 5(3. 14)(4. 84) = 28. 6 + 7. 5988 = 36. 1988 4. 4 m ≈ 36. 2 m 2 6. 5 m

Example Find the area of the sector of a circle below if the radius is 8 units and the central angle is 60°. 8 33. 5 units 2 60°

Example Find the area of the shaded region in the figure if the larger circle has a radius of 4 units and the smaller has a radius of 2 units. 12 units ≈ 37. 68 m 2

Example What happens to the area of a circle if its radius is doubled? The area becomes four times as great.

Example Find the area of the shaded region in the figure if the triangle is an equilateral triangle and the top is a semicircle. 6. 28 units 2 4

Example If the numerical value of the circumference is greater than that of the area, what conclusion can be drawn about the radius? r<2