the minutes hand of a watch 1.5 cm long. How far does it tiks in 40 minutes?
Answers
Answer:
The length of the minute hand is 6.28 cm.
Step-by-step explanation:
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Step-by-step explanation:
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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