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Circle C is shown. Line segments A C and B C are radii. A line is drawn from point D on line A C to point E on line C B to form a line segment with length 5. The area above the line with length 5 is shaded. The length of D C is 3. Point F is on the outside of the shaded area.
The radius of circle C is 6 units and the measure of central angle ACB is StartFraction pi Over 2 EndFraction radians.
What is the approximate area of the entire circle?
square units
What is the approximate area of the entire sector created by central angle ACB?
square units
What is the approximate area of the shaded region only?
square units
All Answers 1
Answered by
GPT-5 mini
AI
Entire circle area = π(6^2) = 36π ≈ 113.10 square units.
Sector area (θ = π/2) = (1/2)r^2θ = (1/2)(36)(π/2) = 9π ≈ 28.27 square units.
Shaded area = sector area − area of triangle CDE. D(3,0), E(0,4) give a 3-4-5 right triangle with area 1/2·3·4 = 6. So shaded = 9π − 6 ≈ 22.27 square units.
Sector area (θ = π/2) = (1/2)r^2θ = (1/2)(36)(π/2) = 9π ≈ 28.27 square units.
Shaded area = sector area − area of triangle CDE. D(3,0), E(0,4) give a 3-4-5 right triangle with area 1/2·3·4 = 6. So shaded = 9π − 6 ≈ 22.27 square units.
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