Question

The area of a quadrant of a circle whose circumference is 22 cm will be:

• A. $\dfrac{44}{7} \text{ cm}^2$
• B. $\dfrac{22}{8} \text{ cm}^2$
• C. $\dfrac{77}{8} \text{ cm}^2$
• D. $\dfrac{8}{77} \text{ cm}^2$

Hint:

To find the area of a quadrant, divide the circle’s area by 4. Use circumference to find the radius first.

Answer 1

The Correct Option is C

Step 1: Find radius.
Circumference $= 2\pi r = 22$. \[ r = \dfrac{22}{2 \times \dfrac{22}{7}} = \dfrac{7}{2} = 3.5 \, \text{cm} \]
Step 2: Area of the circle.
\[ A = \pi r^2 = \dfrac{22}{7} \times (3.5)^2 = \dfrac{22}{7} \times \dfrac{49}{4} = \dfrac{22 \times 7}{4} = 38.5 \, \text{cm}^2 \]
Step 3: Area of a quadrant.
Quadrant = $\dfrac{1}{4}$ of circle’s area. \[ \text{Area of quadrant} = \dfrac{1}{4} \times 38.5 = 9.625 = \dfrac{77}{8} \, \text{cm}^2 \]
Step 4: Conclusion.
Hence, the area of a quadrant of the circle is $\dfrac{77}{8} \, \text{cm}^2$.