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

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Question

(C) The length of the minute hand is the radius of the circle,$r = 10.5 \, cm = \frac{21}{2} \, cm$.The minute hand completes $360^{\circ}$ in $60$ mi

Vedclass · Accepted Answer

$115.5$

Vedclass · Answer

(C) The length of the minute hand is the radius of the circle,$r = 10.5 \, cm = \frac{21}{2} \, cm$.The minute hand completes $360^{\circ}$ in $60$ minutes.In $20$ minutes,the angle swept by the minute hand is $	heta = \frac{360^{\circ}}{60} 	imes 20 = 120^{\circ}$.The area of the region swept is the area of a sector with radius $r$ and central angle $	heta$.Area $= \frac{	heta}{360^{\circ}} 	imes \pi r^2$Area $= \frac{120}{360} 	imes \frac{22}{7} 	imes \left(\frac{21}{2}ight)^2$Area $= \frac{1}{3} 	imes \frac{22}{7} 	imes \frac{21}{2} 	imes \frac{21}{2}$Area $= \frac{1}{3} 	imes 11 	imes 3 	imes \frac{21}{2} = \frac{231}{2} = 115.5 \, cm^2$.

The length of the minute hand of a clock is $10.5 \, cm$. The area of the region swept by it in $20$ minutes is $\ldots \, cm^2$.

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