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sector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector?
sector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector?
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Asector having a central angle of 72 degree is cut from a circular she...
Understanding the Problem
To find the area of a sector with a central angle of 72 degrees from a circular sheet with a circumference of 132 cm, we need to follow specific steps.
Step 1: Calculate the Radius of the Circle
- The formula for the circumference (C) of a circle is given by:
C = 2 * π * r
- Given C = 132 cm, we can rearrange to find the radius (r):
r = C / (2 * π)
- Using π ≈ 3.14, we calculate:
r = 132 / (2 * 3.14)
r ≈ 21 cm
Step 2: Find the Area of the Whole Circle
- The area (A) of a circle is given by:
A = π * r²
- Substituting the radius:
A = 3.14 * (21)²
A ≈ 3.14 * 441
A ≈ 1385.94 cm²
Step 3: Calculate the Area of the Sector
- The area of the sector (A_sector) is a fraction of the total area based on the central angle:
A_sector = (θ/360) * A
- With θ = 72 degrees:
A_sector = (72/360) * 1385.94
A_sector = (1/5) * 1385.94
A_sector ≈ 277.19 cm²
Conclusion
The area of the sector with a central angle of 72 degrees from a circular sheet with a circumference of 132 cm is approximately 277.19 cm². This method combines calculations of the radius, total area, and sector area efficiently.
To find the area of a sector with a central angle of 72 degrees from a circular sheet with a circumference of 132 cm, we need to follow specific steps.
Step 1: Calculate the Radius of the Circle
- The formula for the circumference (C) of a circle is given by:
C = 2 * π * r
- Given C = 132 cm, we can rearrange to find the radius (r):
r = C / (2 * π)
- Using π ≈ 3.14, we calculate:
r = 132 / (2 * 3.14)
r ≈ 21 cm
Step 2: Find the Area of the Whole Circle
- The area (A) of a circle is given by:
A = π * r²
- Substituting the radius:
A = 3.14 * (21)²
A ≈ 3.14 * 441
A ≈ 1385.94 cm²
Step 3: Calculate the Area of the Sector
- The area of the sector (A_sector) is a fraction of the total area based on the central angle:
A_sector = (θ/360) * A
- With θ = 72 degrees:
A_sector = (72/360) * 1385.94
A_sector = (1/5) * 1385.94
A_sector ≈ 277.19 cm²
Conclusion
The area of the sector with a central angle of 72 degrees from a circular sheet with a circumference of 132 cm is approximately 277.19 cm². This method combines calculations of the radius, total area, and sector area efficiently.
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Asector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector?
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Asector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Asector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Asector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector?.
Asector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Asector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Asector having a central angle of 72 degree is cut from a circular sheet who circumference is 132 cm find the area of the sector?.
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