If the circumference of a circle is $22\text{ cm}$, then the area of its quadrant is:
$\dfrac{77}{8}\text{ cm}^2$
$\dfrac{77}{2}\text{ cm}^2$
$\dfrac{77}{4}\text{ cm}^2$
$\dfrac{77}{16}\text{ cm}^2$
Step-by-Step Solution
Key Concept: $2\pi r = 22 \Rightarrow r = 7/2\text{ cm}$. Quadrant area $= \dfrac{1}{4} \pi r^2$.
Stepwise Solution:
$2 \times \dfrac{22}{7} \times r = 22 \Rightarrow r = \dfrac{7}{2}\text{ cm}$. [0.5 Mark]
Quadrant area $= \dfrac{1}{4} \times \dfrac{22}{7} \times \dfrac{49}{4} = \dfrac{77}{8}\text{ cm}^2$. [0.5 Mark]
Marking Scheme:
• Finding radius $r = 7/2\text{ cm}$: 0.5 Mark
• Evaluating quadrant area $= 77/8\text{ cm}^2$: 0.5 Mark
Correct Answer: $\dfrac{77}{8}\text{ cm}^2$