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The area of smaller segment of a circle cut off by chord of length 5cm subtending an angle 30⁰ at the circumference. Find the area of smaller segment convert degree to radian?
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The area of smaller segment of a circle cut off by chord of length 5cm...
Calculation of the area of the smaller segment of a circle
Given
- Length of chord = 5cm
- Angle subtended by the chord at the circumference = 30⁰
Conversion of degree to radian
As the formula for finding the area of a segment of a circle requires the angle to be in radians, we need to convert 30⁰ to radians.
1⁰ = π/180 radians
Therefore, 30⁰ = (30 x π)/180 radians = π/6 radians
Calculation of the area of the segment
The area of a segment of a circle can be calculated using the formula:
Area of segment = (θ/2) x r² - [(r x sinθ)/2]
Where:
- θ = Angle subtended by the chord at the center of the circle (in radians)
- r = Radius of the circle
In this case, we know that:
- θ = π/6 radians
- Length of chord = 5cm
To calculate the radius of the circle, we need to use the formula:
r = (c/2) x (1/sin(θ/2))
Where:
- c = Length of chord
- θ = Angle subtended by the chord at the center of the circle (in radians)
Substituting the given values, we get:
r = (5/2) x (1/sin(π/12))
Using a calculator, we get:
r ≈ 5.77cm
Now, substituting the values of θ and r in the formula for area of segment, we get:
Area of segment = ((π/6)/2) x (5.77)² - [(5.77 x sin(π/6))/2]
Using a calculator, we get:
Area of segment ≈ 1.55cm²
Conclusion
Therefore, the area of the smaller segment of the circle cut off by the chord of length 5cm subtending an angle 30⁰ at the circumference is approximately 1.55cm².
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The area of smaller segment of a circle cut off by chord of length 5cm subtending an angle 30⁰ at the circumference. Find the area of smaller segment convert degree to radian?
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The area of smaller segment of a circle cut off by chord of length 5cm subtending an angle 30⁰ at the circumference. Find the area of smaller segment convert degree to radian? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The area of smaller segment of a circle cut off by chord of length 5cm subtending an angle 30⁰ at the circumference. Find the area of smaller segment convert degree to radian? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of smaller segment of a circle cut off by chord of length 5cm subtending an angle 30⁰ at the circumference. Find the area of smaller segment convert degree to radian?.
The area of smaller segment of a circle cut off by chord of length 5cm subtending an angle 30⁰ at the circumference. Find the area of smaller segment convert degree to radian? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The area of smaller segment of a circle cut off by chord of length 5cm subtending an angle 30⁰ at the circumference. Find the area of smaller segment convert degree to radian? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of smaller segment of a circle cut off by chord of length 5cm subtending an angle 30⁰ at the circumference. Find the area of smaller segment convert degree to radian?.
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