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Sagot :

Answer:

  • 240.73 mm

Step-by-step explanation:

The hour hand is 20 mm and the minute hand is

  • 200% of 20 mm = 2*20 mm = 40 mm long

The tip of the hour hand travels 1/12 of the circle and the tip of the minute hand travels full circle in one hour.

Find each length and their difference using circumference formula.

  • C = 2πr

Hour hand

  • 1/12*(2*3.14*20) = 10.47 mm (rounded)

Minute hand

  • 2*3.14*40 = 251.2 mm

The difference between the two above

  • 251.2 - 10.47 = 240.73 mm

Answer:

230.38 mm

Step-by-step explanation:

The distance traveled by the tip of the hands is (part of) the circumference of the circle with radius of the lengths of the hands.

[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]

Radii

Larger circle (minute hand):  

  • r = 200% of 20 mm = 40 mm

Smaller circle (hour hand):

  • r = 20 mm

Minute Hand

The minute hand does a full rotation of the circle in one hour.

Therefore, the distance it travels in one hour is the complete circumference of a circle with radius 40 mm:

[tex]\begin{aligned} \implies \textsf{Distance minute hand travels} & = \sf 2 \pi (40)\\ & = \sf 80 \pi \: mm\end{aligned}[/tex]

Hour Hand

There are 12 numbers on a clock.

The hour hand travels from one number to the next in one hour.

Therefore, the distance it travels in one hour is 1/12th of the circumference of the circle:

[tex]\begin{aligned}\implies \sf \textsf{Distance hour hand travels} & =\left(\dfrac{1}{12}\right)2 \pi r\\ & = \sf \left(\dfrac{1}{12}\right)2 \pi (40)\\& = \sf \dfrac{20}{3}\pi \: mm \end{aligned}[/tex]

To find how much farther the tip of the minute hand moves than the tip of the hour hand, subtract the latter from the former:

[tex]\begin{aligned}\implies \textsf{distance} & = \textsf{minute hand distance}-\textsf{hour hand distance}\\& = \sf 80 \pi - \dfrac{20}{3} \pi \\& = \sf \dfrac{220}{3} \pi \\& = \sf 230.38\: mm \:(nearest\:hundredth) \end{aligned}[/tex]

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