The length of the minute hand of a clock is 1 | vedclass

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Question

(A) During $60$ minutes ($1$ hour),the minute hand completes one full rotation,i.e.,it subtends an angle of $360^{\circ}$.The time duration from $10.1

Vedclass · Accepted Answer

$205 \frac{1}{3} \, cm^2$

Vedclass · Answer

(A) During $60$ minutes ($1$ hour),the minute hand completes one full rotation,i.e.,it subtends an angle of $360^{\circ}$.The time duration from $10.10 \, AM$ to $10.30 \, AM$ is $20$ minutes.Therefore,the angle $	heta$ subtended by the minute hand in $20$ minutes is:$	heta = \frac{360^{\circ}}{60} 	imes 20 = 120^{\circ}$.The radius $r$ of the sector is the length of the minute hand,which is $14 \, cm$.The area of the sector swept is given by the formula:$	ext{Area} = \frac{\pi r^2 	heta}{360^{\circ}}$Substituting the values:$	ext{Area} = \frac{22}{7} 	imes 14 	imes 14 	imes \frac{120^{\circ}}{360^{\circ}}$$	ext{Area} = \frac{22}{7} 	imes 196 	imes \frac{1}{3}$$	ext{Area} = 22 	imes 28 	imes \frac{1}{3} = \frac{616}{3} \, cm^2$$	ext{Area} = 205 \frac{1}{3} \, cm^2$.

The length of the minute hand of a clock is $14 \, cm$. Find the area of the region swept by it between $10.10 \, AM$ to $10.30 \, AM$.

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