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The area of a quadrant of a circle whose circumference is 88cm is
- a)77 sq. cm
- b)38.5 sq. cm
- c)154 sq. cm
- d)22 sq. cm
Correct answer is option 'C'. Can you explain this answer?
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Understanding the Problem
To find the area of a quadrant of a circle given its circumference, we first need to understand the relationship between circumference, radius, and area.
Step 1: Finding the Radius
- The formula for the circumference (C) of a circle is given by:
C = 2 * π * r
- Given that the circumference is 88 cm:
88 = 2 * π * r
- To find the radius (r), rearrange the formula:
r = 88 / (2 * π)
Step 2: Calculating the Radius
- Using the approximate value of π as 3.14:
r = 88 / (2 * 3.14) = 88 / 6.28 ≈ 14 cm
Step 3: Finding the Area of the Circle
- The area (A) of a circle is given by:
A = π * r²
- Substitute the value of r:
A = π * (14)² = π * 196
Step 4: Calculating the Area
- Using the approximate value of π as 3.14:
A ≈ 3.14 * 196 ≈ 615.44 sq. cm
Step 5: Finding the Area of the Quadrant
- A quadrant is one-fourth of the circle's area:
Area of Quadrant = A / 4
Area of Quadrant ≈ 615.44 / 4 ≈ 153.86 sq. cm
Conclusion
- The closest option to our calculated area is 154 sq. cm, which corresponds to option 'C'.
- Therefore, the correct answer is option 'C'.
This detailed step-by-step process highlights how to derive the area of a circle quadrant from its circumference effectively.
To find the area of a quadrant of a circle given its circumference, we first need to understand the relationship between circumference, radius, and area.
Step 1: Finding the Radius
- The formula for the circumference (C) of a circle is given by:
C = 2 * π * r
- Given that the circumference is 88 cm:
88 = 2 * π * r
- To find the radius (r), rearrange the formula:
r = 88 / (2 * π)
Step 2: Calculating the Radius
- Using the approximate value of π as 3.14:
r = 88 / (2 * 3.14) = 88 / 6.28 ≈ 14 cm
Step 3: Finding the Area of the Circle
- The area (A) of a circle is given by:
A = π * r²
- Substitute the value of r:
A = π * (14)² = π * 196
Step 4: Calculating the Area
- Using the approximate value of π as 3.14:
A ≈ 3.14 * 196 ≈ 615.44 sq. cm
Step 5: Finding the Area of the Quadrant
- A quadrant is one-fourth of the circle's area:
Area of Quadrant = A / 4
Area of Quadrant ≈ 615.44 / 4 ≈ 153.86 sq. cm
Conclusion
- The closest option to our calculated area is 154 sq. cm, which corresponds to option 'C'.
- Therefore, the correct answer is option 'C'.
This detailed step-by-step process highlights how to derive the area of a circle quadrant from its circumference effectively.
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The area of a quadrant of a circle whose circumference is 88cm isa)77 sq. cmb)38.5 sq. cmc)154 sq. cmd)22 sq. cmCorrect answer is option 'C'. Can you explain this answer?
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The area of a quadrant of a circle whose circumference is 88cm isa)77 sq. cmb)38.5 sq. cmc)154 sq. cmd)22 sq. cmCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The area of a quadrant of a circle whose circumference is 88cm isa)77 sq. cmb)38.5 sq. cmc)154 sq. cmd)22 sq. cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a quadrant of a circle whose circumference is 88cm isa)77 sq. cmb)38.5 sq. cmc)154 sq. cmd)22 sq. cmCorrect answer is option 'C'. Can you explain this answer?.
The area of a quadrant of a circle whose circumference is 88cm isa)77 sq. cmb)38.5 sq. cmc)154 sq. cmd)22 sq. cmCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The area of a quadrant of a circle whose circumference is 88cm isa)77 sq. cmb)38.5 sq. cmc)154 sq. cmd)22 sq. cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a quadrant of a circle whose circumference is 88cm isa)77 sq. cmb)38.5 sq. cmc)154 sq. cmd)22 sq. cmCorrect answer is option 'C'. Can you explain this answer?.
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