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

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Solution

$L e n g t h o f t h e m i n u t e h a n d o f a c l o c k,$ $r = 14 c m$ .
$A r e a s w e p t b y t h e m i n u t e h a n d i n$ $5$ $m i n u t e s$ $= 360 \times \frac{5}{60}$ $= 30^{o}$
$A n g l e o f s e g m e n t o f a c i r c l e,$ $θ = 30^{o}$
$∴$ $A r e a s w e p t b y t h e m i n u t e h a n d i n$ $5$ $m i n u t e,$
$= \frac{θ}{360} \times π r^{2}$
$= \frac{30}{360} \times \frac{22}{7} \times (14)^{2}$
$= \frac{1}{12} \times 28 \times 22$
$= \frac{154}{3} c m^{2}$

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