A circle wire clip of radius 7mm with a gap of 7mm between the ends. Calculate the total length of wire in clip to the nearest mm, given that about 4mm are used altogether in making the turnovers at the ends.
The length of wire in the clip can be calculated by finding the circumference of the circle and subtracting the gap between the ends:
Circumference = 2πr
Circumference = 2π(7mm)
Circumference = 44mm
Total length of wire = 44mm - 7mm (gap) + 2(4mm) (turnovers)
Total length of wire = 44mm - 7mm + 8mm
Total length of wire = 45mm (rounded to nearest mm)
Therefore, the total length of wire in the clip is about 45mm.
To calculate the total length of wire in the clip, we need to find the circumference of the circle.
Step 1: Calculate the circumference of the circle wire clip
The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * radius
Given that the radius is 7mm, we can substitute it into the formula:
Circumference = 2 * π * 7
Step 2: Calculate the total length of wire without accounting for the gap and turnovers
Using the formula from Step 1, we can calculate the total length of wire without considering the gap and turnovers:
Total length without gap = Circumference = 2 * π * 7
Step 3: Subtract the gap and turnovers
From the total length calculated in Step 2, we need to subtract the length of the gap and the length used for the turnovers.
Total length with gap and turnovers = Total length without gap - gap length - turnover length
Given that the gap is 7mm and the turnovers use about 4mm altogether, we can substitute these values into the formula:
Total length with gap and turnovers = 2 * π * 7 - 7 - 4
Finally, let's calculate the result:
Total length with gap and turnovers ≈ 43 mm
Therefore, the total length of wire in the clip, accounting for the gap and turnovers, is approximately 43 mm.