Question

If the circumference of a circle is 22 cm, then the area of a quadrant of the circle is

• A. 8.625 sq.cm
• B. 9.625 sq.cm
• C. 10.5 sq.cm
• D. 12.825 sq.cm

Answer 1

The Correct Option is B

Step 1: Recall the formula for the circumference of a circle.

The circumference of a circle is given by:

\[ C = 2\pi r, \]

where \( r \) is the radius of the circle. Substituting \( C = 22 \):

\[ 2\pi r = 22. \]

Solve for \( r \):

\[ r = \frac{22}{2\pi}. \]

Using \( \pi = \frac{22}{7} \):

\[ r = \frac{22}{2 \cdot \frac{22}{7}} = \frac{22 \cdot 7}{44} = \frac{7}{2} = 3.5 \, \text{cm}. \]

Step 2: Find the area of the circle.

The area of a circle is given by:

\[ A = \pi r^2. \]

Substitute \( r = 3.5 \):

\[ A = \pi (3.5)^2 = \pi \cdot 12.25. \]

Using \( \pi = \frac{22}{7} \):

\[ A = \frac{22}{7} \cdot 12.25 = 22 \cdot 1.75 = 38.5 \, \text{sq. cm}. \]

Step 3: Find the area of a quadrant.

A quadrant is one-fourth of the circle's area:

\[ \text{Area of quadrant} = \frac{1}{4} \cdot A = \frac{1}{4} \cdot 38.5 = 9.625 \, \text{sq. cm}. \]

Final Answer: The area of the quadrant is \( \mathbf{9.625 \, \text{sq. cm}} \), which corresponds to option \( \mathbf{(2)} \).