The length of the minute hand of a clock is $14\text{ cm}$. The area swept by the minute hand in $5$ minutes is:
$\dfrac{154}{3}\text{ cm}^2$
$\dfrac{154}{9}\text{ cm}^2$
$\dfrac{77}{3}\text{ cm}^2$
$\dfrac{77}{6}\text{ cm}^2$
Step-by-Step Solution
Key Concept: In 60 minutes, minute hand sweeps $360^\circ \Rightarrow$ in 5 minutes, $\theta = \dfrac{360^\circ}{60} \times 5 = 30^\circ$.
Stepwise Solution:
$\theta = 30^\circ$. Area $= \dfrac{30^\circ}{360^\circ} \times \dfrac{22}{7} \times 14 \times 14$. [0.5 Mark]
$= \dfrac{1}{12} \times 22 \times 28 = \dfrac{616}{12} = \dfrac{154}{3}\text{ cm}^2$. [0.5 Mark]
Marking Scheme:
• Finding angle $\theta = 30^\circ$: 0.5 Mark
• Evaluating area $= 154/3\text{ cm}^2$: 0.5 Mark
Correct Answer: $\dfrac{154}{3}\text{ cm}^2$