The length of the minute hand of a clock is $14\text{ cm}$. Find the area swept by the minute hand in $5$ minutes.
Step-by-Step Solution
Key Concept: Angle in 5 minutes $= \dfrac{360^\circ}{60} \times 5 = 30^\circ$. Area $= \dfrac{30}{360} \times \dfrac{22}{7} \times 14^2 = \dfrac{1}{12} \times \dfrac{22}{7} \times 196 = \dfrac{154}{3}\text{ cm}^2 = 51.33\text{ cm}^2$.
$\theta = \dfrac{360^\circ}{60} \times 5 = 30^\circ$. [0.5 Mark]
$\text{Area} = \dfrac{30}{360} \times \dfrac{22}{7} \times 196 = \dfrac{1}{12} \times 616 = \dfrac{154}{3}\text{ cm}^2$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Finding central angle $\theta = 30^\circ$: 0.5 Mark
Evaluating swept area $= 154/3\text{ cm}^2$: 1.5 Marks
Correct Answer: