The minute- hand of clock is 6cm long.how far does the end of the hand travel in 35 minutes?
The minute hand completes one full rotation in 60 minutes. Therefore, in 35 minutes, it will travel a fraction of a full rotation:
fraction of rotation = 35/60 = 7/12
To find the distance traveled by the end of the hand, we need to find the circumference of the circle it traces:
circumference = 2πr
where r is the length of the minute hand (6cm). Substituting in this value and simplifying:
circumference = 2π × 6 = 12π cm
The distance traveled by the end of the hand is therefore:
distance = fraction of rotation × circumference
distance = (7/12) × 12π
distance = 7π cm
Therefore, the end of the minute hand travels 7π cm in 35 minutes.
To calculate the distance traveled by the end of the minute hand in 35 minutes, we can consider the circumference of a circle with a radius equal to the length of the minute hand.
The formula for the circumference of a circle is given by: C = 2πr, where C is the circumference and r is the radius.
In this case, the radius is equal to 6 cm.
So, the circumference of the circle is: C = 2π(6) = 12π cm.
Since the minute hand completes one full revolution around the clock in 60 minutes, we need to find what fraction of the full circumference is covered in 35 minutes.
Let's calculate the fraction: Fraction = 35 / 60 = 7 / 12.
Now, we can calculate the distance traveled by the end of the minute hand in 35 minutes by multiplying the fraction of the circumference covered by the full circumference.
Distance = Fraction * Circumference
= (7 / 12) * (12π cm)
= 7π cm.
Therefore, the end of the minute hand travels a distance of 7π cm in 35 minutes.