The minute hand of a clock is 6cm long . how far does the end of the hand travel in 35 minutes
In 1 minute, the minute hand travels the entire circumference of the clock face, which has a radius of 6cm (the length of the minute hand). Therefore, the distance traveled in 1 minute is:
circumference = 2 x π x radius = 2 x π x 6cm ≈ 37.7cm
So in 35 minutes, the distance traveled by the end of the hand is:
distance = 37.7cm x 35 = 1319.5cm (to one decimal place)
Therefore, the end of the minute hand travels approximately 1319.5cm in 35 minutes.
Now bot, what kind of sense does your answer make???
the whole distance around is only 37.7 , so how can the minute hand
travel 1319.5 cm in only 35 minutes ????
Guess the bot is too embarrassed to answer.
distance = (35/60)(2π(6)) cm = 21.99 cm or appr 22 cm
I apologize for my mistake in the previous response. You are correct, the distance traveled by the end of the minute hand in 35 minutes can be calculated using the formula for the length of an arc:
distance = (angle/360) x 2πr
where angle is the angle formed by the minute hand and the 12 o'clock position, r is the length of the minute hand, and 360 is the number of degrees in a full circle.
In 35 minutes, the minute hand moves 35/60 or 7/12 of the way around the clock face, which is an angle of:
angle = (7/12) x 360 = 210 degrees
Substituting the values into the formula:
distance = (210/360) x 2π x 6 cm = 22.0 cm (rounded to one decimal place)
Therefore, the end of the minute hand travels approximately 22.0 cm in 35 minutes. Again, I apologize for my previous error.
To find out how far the end of the hand travels in 35 minutes, we need to determine the distance covered by the end of the minute hand when it completes one full rotation.
The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius.
In this case, the length of the minute hand is given as 6 cm, which represents the radius of the circle. Therefore, the circumference of the circle traced by the end of the minute hand is 2π(6) = 12π cm.
Since the minute hand takes 60 minutes to complete a full rotation, we can calculate how far it travels in 35 minutes by setting up a proportion:
Distance covered in 35 minutes / Distance covered in 60 minutes = 35 / 60
Let x be the distance covered in 35 minutes:
x / 12π = 35 / 60
To solve for x, we can cross-multiply:
x = (12π * 35) / 60
Calculating this expression gives us the distance covered in 35 minutes:
x ≈ 21.99 cm (rounded to the nearest hundredth)
Therefore, the end of the hand travels approximately 21.99 cm in 35 minutes.
To find out how far the end of the minute hand travels in 35 minutes, we need to calculate the circumference of the circle it traces.
The minute hand of a clock goes around the clock face in 60 minutes, which is equivalent to 360 degrees. Since 360 degrees is equal to the circumference of a circle, we can use this information to calculate the distance traveled by the end of the hand in one minute.
We know that the minute hand is 6 cm long. The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius.
In this case, the radius of the circle is the length of the minute hand, which is 6 cm. So, the circumference of the circle the end of the minute hand travels in one minute is:
C = 2π(6 cm)
C ≈ 2(3.14)(6 cm)
C ≈ 37.68 cm
Now that we know the distance traveled by the end of the minute hand in one minute is approximately 37.68 cm, we can calculate the distance traveled in 35 minutes by multiplying this distance by 35:
Distance = 37.68 cm × 35 minutes
Distance ≈ 1318.8 cm
Therefore, the end of the minute hand travels approximately 1318.8 cm in 35 minutes.