If the hour hand of a clock is 7 inches long, how many inches does the tip travel between 1:00 PM and 4:00 PM?
That would depend upon the size of the clock face.
It does not say.
Does your problem want to know how many inches or degrees the minute hand travels?
Inches, rounded to 2 decimal places.
If the 7-inch hand goes through a complete circle, it would travel the equivalent of the circumference of a circle of radius 7 inches.
Use Circumference = 2πr
How far would the tip travel from 1 to 4 o'clock?
I got circumference = 43.96. How would I find how many inches it travels from 1 to 4?
Every 5 minutes, the minutes hand turns 30°
If it turns 360° (from 12 to 12), then the distance is 43.96.
You can use proportions to find how much distance the tip travels from 1 to 4.
thanks
To determine how many inches the tip of the hour hand travels between 1:00 PM and 4:00 PM, we need to calculate the angular displacement of the hour hand during that period.
The hour hand completes a full revolution (360 degrees) in 12 hours. Therefore, in one hour, it covers an angular displacement of 360/12 = 30 degrees.
Between 1:00 PM and 4:00 PM, there are 3 hours in total. So, the hour hand covers a total angular displacement of 3 * 30 = 90 degrees.
To find out the linear distance, or the number of inches the tip of the hour hand travels, we need to calculate the arc length of the circular path traced by the tip.
The arc length is given by the formula: arc length = (radius) * (angle in radians)
In this case, the radius is given as 7 inches and the angle is 90 degrees. However, we need to convert the angle from degrees to radians before using the formula.
Since there are 2π radians in a circle (360 degrees), we can convert the angle in radians using the formula: angle in radians = (angle in degrees) * (π / 180)
Substituting the values, we have: angle in radians = 90 * (π / 180) = π / 2
Now, we can use the formula to calculate the arc length: arc length = (7 inches) * (π / 2) = (7π / 2) inches ≈ 10.99 inches.
Therefore, the tip of the hour hand travels approximately 10.99 inches between 1:00 PM and 4:00 PM.