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. 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.

circumference diameter C = 2pr C = pd circumference diameter = p

Area of a circle A = pr2 The area of a circle (A) is the product of p and the square of the radius (r).

Example 1 Find the area of a circle whose radius is 3 km. A = pr2 = 3.14(9) ≈ 28.3 km2

Example 2 Find the area of a circle whose diameter is 5 m. r = = = 2.5 5 2 A = pr2 = p(2.52) = 3.14(6.25) ≈ 19.6 m2

Example Find the area of a circle with a radius of 5 units. 25p units2

Example Find the area of a circle with a diameter of 12 units. 36p units2

Example Find the radius of a circle if its area is 191 units2.

Example Find the area of a circle if its circumference is 62.8 units.

Example Find the circumference of a circle if its area is 277.45 units2. 59 units

Example 3 Find the area of the colored region. A = pR2 − pr2 = p(62) − p(42) = 36p − 16p = (36 − 16)p = 20p = 20(3.14) ≈ 62.8 m2

Example 4 Find the area of the figure. A = bh + pr2 1 2 = 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 m2 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°. 60° 8 33.5 units2

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 m2

The area becomes four times as great. 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. 4 6.28 units2

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