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

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(B) The length of the minute hand $(r)$ is $10.5 \, cm$.The time interval between $2.25 \, PM$ and $2.40 \, PM$ is $15 \, 	ext{minutes}$.$A$ minute h

Vedclass · Accepted Answer

$86.625$

Vedclass · Answer

(B) The length of the minute hand $(r)$ is $10.5 \, cm$.The time interval between $2.25 \, PM$ and $2.40 \, PM$ is $15 \, 	ext{minutes}$.$A$ minute hand completes a full circle $(360^{\circ})$ in $60 \, 	ext{minutes}$.Therefore,the angle swept in $15 \, 	ext{minutes}$ is $	heta = (15/60) 	imes 360^{\circ} = 90^{\circ}$.The area swept by the minute hand is the area of a sector with radius $r = 10.5 \, cm$ and angle $	heta = 90^{\circ}$.Area $= (	heta / 360^{\circ}) 	imes \pi r^2 = (90^{\circ} / 360^{\circ}) 	imes (22/7) 	imes 10.5 	imes 10.5$.Area $= (1/4) 	imes (22/7) 	imes 10.5 	imes 10.5 = (1/4) 	imes 22 	imes 1.5 	imes 10.5$.Area $= 0.25 	imes 22 	imes 15.75 = 5.5 	imes 15.75 = 86.625 \, cm^2$.

The length of the minute hand of a clock is $10.5 \, cm$. Find the area of the region swept by it between $2.25 \, PM$ and $2.40 \, PM$. (in $cm^2$)

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