Assuming the earth is a perfect sphere of raius 3950 miles, find (in inches) d. d, is the difference between the arc and a straight line.
what arc, what straight line?
straight line has a distance of 1 mile
To find the difference (d) between the arc and a straight line on a perfect sphere, we can use the formula for the difference between the circumference of a circle and the diameter. Here's how you can calculate it:
1. Convert the radius of the Earth from miles to inches:
- 1 mile is equal to 63,360 inches.
- So, the radius of the Earth in inches is 3950 miles * 63,360 inches/mile = 249,804,000 inches.
2. Calculate the circumference of the Earth:
- The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
- So, the circumference of the Earth is 2 * π * 249,804,000 inches = 1,570,796,321 inches (approximately).
3. Calculate the diameter of the Earth:
- The formula for the diameter of a circle is d = 2r, where d is the diameter and r is the radius.
- So, the diameter of the Earth is 2 * 249,804,000 inches = 499,608,000 inches.
4. Calculate the difference (d) between the arc and a straight line:
- The difference (d) is equal to the circumference (C) minus the diameter (d) of the Earth.
- Therefore, d = 1,570,796,321 inches - 499,608,000 inches = 1,071,188,321 inches.
So, the difference (d) between the arc and a straight line on a perfect sphere with a radius of 3950 miles is approximately 1,071,188,321 inches.