The 144-fiber telephone cable has a 12.7-mm diameter. A 900-pair copper cable has about a 70-mm diameter. Compute the ratio of the cross-sectional area of these two types of transmission lines.
what is (70/12.7)^2 ?
A=πr²
A=π(d/2)²
i): For 144- fiber telephone cable:
A=π(12.7mm/2)²
A=126.65micrometer
ii): For 900-pair copper cable
A'=π( 70mm/2)²
A'= 3847.72micrometer
Now ratio:
A'/A= 126.65/3847.72
= 30.3
To compute the ratio of the cross-sectional areas of the two types of transmission lines, we need to first determine the cross-sectional area of each line.
For the 144-fiber telephone cable:
- Given diameter = 12.7 mm
- Radius = diameter/2 = 12.7 mm/2 = 6.35 mm
To compute the cross-sectional area of a circle, we use the formula:
Area = π * radius^2
Substituting the values, we get:
Area of the 144-fiber telephone cable = π * (6.35 mm)^2
Now, for the 900-pair copper cable:
- Given diameter = 70 mm
- Radius = diameter/2 = 70 mm/2 = 35 mm
Again, using the formula for the cross-sectional area of a circle:
Area of the 900-pair copper cable = π * (35 mm)^2
Finally, to compute the ratio of the two cross-sectional areas:
Ratio = (Area of the 144-fiber telephone cable) / (Area of the 900-pair copper cable)
You can now substitute the values in the formulas and calculate the ratio.
To compute the ratio of the cross-sectional area of these two types of transmission lines, we need to calculate the area of each type of cable.
1. The cross-sectional area of the 144-fiber telephone cable:
Given that the diameter of the cable is 12.7 mm, we can calculate the radius as half the diameter, which is 6.35 mm (since 12.7 mm / 2 = 6.35 mm).
The formula for calculating the area of a circle is A = πr^2, where A represents the area and r is the radius.
Using this formula, we can calculate the area of the 144-fiber cable:
A1 = π * (6.35 mm)^2
2. The cross-sectional area of the 900-pair copper cable:
Given that the diameter of the cable is 70 mm, we can calculate the radius as half the diameter, which is 35 mm (since 70 mm / 2 = 35 mm).
Using the same formula for the area of a circle, we can calculate the area of the 900-pair copper cable:
A2 = π * (35 mm)^2
Now, we can calculate the ratio of the cross-sectional areas:
Ratio = A2 / A1
Let's substitute the values and calculate the ratio.