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Find the area of a quadrant of a circle whose circumference is 22 cm.
Sol: Let the radius of the circle = r
∴ 2πr = 22

⇒ 
how did we get 2πr^2 here ?
Sol: Let the radius of the circle = r
∴ 2πr = 22

⇒ 
how did we get 2πr^2 here ?
Most Upvoted Answer
Find the area of a quadrant of a circle whose circumference is 22 cm.S...
To find the area of a quadrant of a circle whose circumference is given, we need to first determine the radius of the circle. Here’s a detailed breakdown of the solution:
Step 1: Understand the Circumference Formula
The circumference \(C\) of a circle is given by the formula:
\[
C = 2\pi r
\]
where \(r\) is the radius of the circle.
Step 2: Set Up the Equation
Given that the circumference is 22 cm, we can set up the equation:
\[
2\pi r = 22
\]
Step 3: Solve for the Radius
To find the radius \(r\), we can rearrange the equation:
\[
r = \frac{22}{2\pi}
\]
Calculating this gives:
\[
r = \frac{11}{\pi}
\]
Step 4: Calculate the Area of the Circle
The area \(A\) of a circle is calculated using the formula:
\[
A = \pi r^2
\]
Substituting \(r\) into this formula:
\[
A = \pi \left(\frac{11}{\pi}\right)^2
\]
This simplifies to:
\[
A = \pi \cdot \frac{121}{\pi^2} = \frac{121}{\pi}
\]
Step 5: Find the Area of the Quadrant
A quadrant is one-fourth of the area of a circle. Therefore, the area of the quadrant \(A_q\) is:
\[
A_q = \frac{1}{4} A = \frac{1}{4} \cdot \frac{121}{\pi} = \frac{121}{4\pi}
\]
Conclusion
The area of the quadrant of the circle is:
\[
A_q = \frac{121}{4\pi} \text{ cm}^2
\]
This completes the calculation of the area of the quadrant based on the given circumference.
Step 1: Understand the Circumference Formula
The circumference \(C\) of a circle is given by the formula:
\[
C = 2\pi r
\]
where \(r\) is the radius of the circle.
Step 2: Set Up the Equation
Given that the circumference is 22 cm, we can set up the equation:
\[
2\pi r = 22
\]
Step 3: Solve for the Radius
To find the radius \(r\), we can rearrange the equation:
\[
r = \frac{22}{2\pi}
\]
Calculating this gives:
\[
r = \frac{11}{\pi}
\]
Step 4: Calculate the Area of the Circle
The area \(A\) of a circle is calculated using the formula:
\[
A = \pi r^2
\]
Substituting \(r\) into this formula:
\[
A = \pi \left(\frac{11}{\pi}\right)^2
\]
This simplifies to:
\[
A = \pi \cdot \frac{121}{\pi^2} = \frac{121}{\pi}
\]
Step 5: Find the Area of the Quadrant
A quadrant is one-fourth of the area of a circle. Therefore, the area of the quadrant \(A_q\) is:
\[
A_q = \frac{1}{4} A = \frac{1}{4} \cdot \frac{121}{\pi} = \frac{121}{4\pi}
\]
Conclusion
The area of the quadrant of the circle is:
\[
A_q = \frac{121}{4\pi} \text{ cm}^2
\]
This completes the calculation of the area of the quadrant based on the given circumference.
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Find the area of a quadrant of a circle whose circumference is 22 cm.Sol: Let the radius of the circle = r∴ 2πr = 22⇒ how did we get 2πr^2 here ?
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Find the area of a quadrant of a circle whose circumference is 22 cm.Sol: Let the radius of the circle = r∴ 2πr = 22⇒ how did we get 2πr^2 here ? 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 Find the area of a quadrant of a circle whose circumference is 22 cm.Sol: Let the radius of the circle = r∴ 2πr = 22⇒ how did we get 2πr^2 here ? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of a quadrant of a circle whose circumference is 22 cm.Sol: Let the radius of the circle = r∴ 2πr = 22⇒ how did we get 2πr^2 here ?.
Find the area of a quadrant of a circle whose circumference is 22 cm.Sol: Let the radius of the circle = r∴ 2πr = 22⇒ how did we get 2πr^2 here ? 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 Find the area of a quadrant of a circle whose circumference is 22 cm.Sol: Let the radius of the circle = r∴ 2πr = 22⇒ how did we get 2πr^2 here ? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of a quadrant of a circle whose circumference is 22 cm.Sol: Let the radius of the circle = r∴ 2πr = 22⇒ how did we get 2πr^2 here ?.
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