The distance that the tip of the hand travels as it moves from the 12 to the 3 will be 15.7143 cm.
An arc is a smooth curve that joins two endpoints. The arc is mostly referred to as a part of the circle.
As it is given that the length of the hand of the clock is 10 cm, and the movement of the hand of the clock is from 12 to 3 therefore, the movement is about 90°.
Now, if we see the movement of the hand of the clock it will be along the arc of the circle, therefore, the length of the arc with a radius of 10 cm and angle of 90° can be written as,
[tex]\text{Length of the arc} = 2\pi r \times \dfrac{\theta}{360^o}[/tex]
[tex]= 2 \times \pi \times 10 \times\dfrac{90}{360}\\\\= 2 \times \pi \times 10 \times\dfrac{1}{4}\\\\= 15.7143\rm\ cm[/tex]
Hence, the distance that the tip of the hand travels as it moves from the 12 to the 3 will be 15.7143 cm.
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