A piece of wire is wound exactly 100 times around a circular tube with a radius of 9.8 centimeters. Find the length of the piece of wire in meters.
To find the length of the piece of wire, we need to calculate the circumference of the circle formed by the circular tube and then multiply it by the number of times the wire is wound around the tube.
The formula for the circumference of a circle is given by:
C = 2πr
Where C is the circumference and r is the radius of the circle.
In this case, the radius of the circular tube is given as 9.8 centimeters. Since the question asks for the length in meters, it is important to convert the radius to meters.
1 meter = 100 centimeters
So, 9.8 centimeters = 9.8/100 = 0.098 meters (approximately)
Now, we can plug in the values into the formula:
C = 2π(0.098)
To find the value of π, you can use an approximation such as 3.14.
C = 2 * 3.14 * 0.098
C = 0.6152 meters (approximately)
Now, to find the length of the wire, we need to multiply the circumference by the number of times the wire is wound around the tube, which is 100.
Length of wire = C * number of windings
Length of wire = 0.6152 * 100
Length of wire = 61.52 meters
Therefore, the length of the piece of wire is approximately 61.52 meters.