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the minute hand of a watch is 1.4 cm long the tip of the needle moves in 20 minutes a distance equal to |
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Answer» ong>Answer: Answer: The length of the minute hand is 6.28 cm. Step-by-step EXPLANATION: GIVEN : The minute hand of a WATCH is 1.5 cm long. To find : How far does its tip move in 40 minutes? Solution : The minute hand of a watch is 1.5 cm long. i.r. r= 1.5 cm We know that, l=r\times\thetal=r×θ Where, r is the radius l is the length of arc \thetaθ is the angle subtended. Now, Minute hand MAKE 1 revolution in 1 hour. i.e. Minute hand complete 360° in 1 hour. So degree complete in 1 minute = \frac{360}{60} 60 360
Degree complete in 40 minute = \frac{360}{60}\times 40 60 360
×40 Degree complete in 40 minute = 240° In radian measure, \theta=\frac{\pi}{180}\times240θ= 180 π
×240 \theta=\frac{4\pi}{3}θ= 3 4π
SUBSTITUTE the value in the formula, l=r\times\thetal=r×θ l=1.5\times\frac{4\pi}{3}l=1.5× 3 4π
l=2\pil=2π l=2\times 3.14l=2×3.14 l=6.28l=6.28 Therefore, The length of the minute hand is 6.28 cm. |
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