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Question

The length of the minute hand of a clock is $$14$$ cm. Find the area swept by the minute hand in $$5$$ minutes


Solution

In $$60$$ minutes, minute hand completes $$360^0$$ i.e., one rotation.

$$\Rightarrow$$ in $$1$$ minute, minute hands completes $$\dfrac{360^\circ}{60}=6^\circ$$ 

Hence, in $$5$$ minutes the angle covered is is $$6\times 5=30^o$$.

The angle of sector formed is $$30^o$$.

The area swept by the minute hand in $$5$$ minutes$$= \dfrac{30}{360}\times \pi \times 14 \times 14$$ 

Using $$\pi = \dfrac{22}7$$, we get

The area swept by the minute hand in $$5$$ minutes $$=\dfrac{154}3$$ sq. cm

492698_465201_ans_ce4d10966623492499296740db11ed11.png

Mathematics
NCERT
Standard X

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