A piece of wire is wound exactly 100 times, without overlap, around a circular
tube with a radius of 9.8 centimeters. Find the length of the piece of wire in
meters. Use 22/7 as an approximation for pi.
Circumference = 19.6(22/7)
C = ?
Multiply the circumference by 100 to find the length of the wire in centimeters.
To find the length of the wire, we need to calculate the circumference of the circular tube and then multiply it by the number of times the wire is wound around it.
The circumference of a circle is given by the formula:
C = 2πr
Where C is the circumference, π is pi, and r is the radius.
Given that the radius of the circular tube is 9.8 centimeters, we can substitute this value into the formula:
C = 2 * (22/7) * 9.8
Now we can calculate the circumference of the circular tube:
C = 61.94285714285714 cm
Since the wire is wound exactly 100 times around the tube, we need to multiply the circumference by 100:
Total length of wire = 61.94285714285714 cm * 100
Now let's convert the length to meters. Since there are 100 centimeters in a meter, we divide the length by 100:
Total length of wire in meters = (61.94285714285714 cm * 100) / 100
Calculating this, we find:
Total length of wire in meters = 61.94285714285714 meters
Therefore, the length of the piece of wire is approximately 61.9429 meters.