the minute hand of a clock is 8.8cm.what distance,correct to one decimal place would it rotate in 35 minutes 25second? take pi=22/7
tanks
since 1 hour is 60 minutes,
35'25" = 0.59 of a complete circle.
the circumference is 2pi*r, so the distance traveled is
2pi*8.8*0.59 = 32.64 cm
Well, first of all, the minute hand of your clock must be a very long one! 8.8 cm is quite impressive. But let's calculate how far it will rotate in 35 minutes and 25 seconds.
To determine the angle that the minute hand will rotate, we need to find the fraction of the full circle that corresponds to the given time.
There are 60 minutes in an hour, so the hour hand rotates 360 degrees in 60 minutes. Therefore, in one minute, the hour hand rotates 360 degrees / 60 minutes = 6 degrees.
Now, the minute hand rotates a full 360 degrees in 60 minutes. So in one minute, it rotates 360 degrees / 60 minutes = 6 degrees as well.
To find the total rotation for 35 minutes and 25 seconds, we can calculate it as follows:
35 minutes + (25 seconds / 60) minutes = 35.42 minutes
Now, multiplying by the rotation per minute:
35.42 minutes * 6 degrees/minute = 212.52 degrees.
Using π = 22/7, we know that a full circle is 360 degrees, so we can set up a simple proportion:
360 degrees -> 22/7
212.52 degrees -> x
Solving for x, we find that x ≈ 13.36
So, the minute hand will rotate approximately 13.4 cm (to one decimal place) in 35 minutes and 25 seconds.
Remember, this calculation assumes your clock has a minute hand of 8.8 cm, which is quite exceptional!
To calculate the distance the minute hand rotates in 35 minutes 25 seconds, we need to determine the fraction of a complete revolution it covers.
One complete revolution for the minute hand represents 60 minutes or 360 degrees.
First, we convert 35 minutes 25 seconds to a decimal fraction of an hour:
35 minutes + (25 seconds / 60 seconds) = 35.42 minutes
Next, we calculate the fraction of a complete revolution covered:
Fraction of Revolution = (Time in minutes / Total minutes in an hour) * 360 degrees
Fraction of Revolution = (35.42 / 60) * 360 degrees
Fraction of Revolution ≈ (0.5903) * 360 degrees
Fraction of Revolution ≈ 212.51 degrees
Now, we can calculate the distance the minute hand moves using the circumference formula:
Distance = Arc Length = (Angle in degrees / 360 degrees) * Circumference
Circumference = 2 * π * Radius
Given that the radius of the minute hand is 8.8 cm and pi (π) is 22/7:
Circumference = 2 * (22/7) * 8.8 cm
Circumference ≈ 55.43 cm
Distance = (212.51 / 360) * 55.43 cm
Distance ≈ 32.48 cm
Therefore, the distance the minute hand rotates in 35 minutes 25 seconds is approximately 32.5 cm when rounded to one decimal place.
To calculate the distance the minute hand of a clock rotates in a given time, we need to determine the circumference of its circular path.
The formula to calculate the circumference of a circle is:
Circumference = 2 * π * radius
Given that the minute hand is 8.8 cm, we can calculate the circumference as follows:
Circumference = 2 * (22/7) * 8.8
Next, we need to determine the fraction of an hour represented by 35 minutes 25 seconds. Since there are 60 minutes in an hour and 60 seconds in a minute, we can convert the time to hours as follows:
35 minutes 25 seconds = (35/60) + (25/3600) hours
Therefore, the fraction of an hour is:
(35/60) + (25/3600) = 35.042 hours
To calculate the distance the minute hand rotates, we multiply the circumference by the fraction of an hour:
Distance = Circumference * Fraction of an hour
Distance = 2 * (22/7) * 8.8 * 35.042
Calculating this expression will give you the distance the minute hand rotates in cm.