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Published bySpencer Patterson Modified over 5 years ago

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

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Exercise Find the radius of a circle if the diameter is 5 in. 2.5 in.

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

8 cm ≈ cm

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Exercise Find the circumference of a circle if the radius is 10 cm.

20 cm ≈ 62.8 cm

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Exercise Find the radius of a circle if the circumference is 31.4 in.

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circumference diameter

C = 2pr C = pd circumference diameter = p

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

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Example 1 Find the area of a circle whose radius is 3 km. A = pr2

= 3.14(9) ≈ 28.3 km2

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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

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

25p units2

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

36p units2

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

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

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

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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

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Example 4 Find the area of the figure. A = bh + pr2

1 2 = 6.5(4.4) + 0.5(3.14)(2.22) = (3.14)(4.84) = = 4.4 m ≈ 36.2 m2 6.5 m

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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

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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 ≈ m2

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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.

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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

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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

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