# Thread: Calculating Distance between 2 circles

1. ## Calculating Distance between 2 circles

The answer right below the question is the answer, but I am unsure as to why we are dividing the entire problem by 2

2. ## Re: Calculating Distance between 2 circles

Originally Posted by KingNathan
The answer right below the question is the answer, but I am unsure as to why we are dividing the entire problem by 2
It's because the conveyor belt goes all the way around.
The conveyor belt length is the distance between the centres twice,
and a semicircle twice.
Hence the distance between the centres is half of "15 feet minus 2 semicircle lengths".
The diameters of the circles is 1 foot, so their radii is 1/2 a foot.
Finish up by calculating the length of the round part of the belt.

3. ## Re: Calculating Distance between 2 circles

It's because the conveyor belt goes all the way around.
The conveyor belt length is the distance between the centres twice,
and a semicircle twice.
Hence the distance between the centres is half of "15 feet minus 2 semicircle lengths".
The diameters of the circles is 1 foot, so their radii is 1/2 a foot.
Finish up by calculating the length of the round part of the belt.
That completely makes sense for me in cutting the entire distance of the belt in half. But then that would leave me with half of the figure left, correct?

At this point, how do I wind up with pie in the numerator of the final answer?

4. ## Re: Calculating Distance between 2 circles

That's another way to arrive at the answer.
You now only need to subtract the circumferences of 2 quarter-circles.

5. ## Re: Calculating Distance between 2 circles

That's another way to arrive at the answer.
You now only need to subtract the circumferences of 2 quarter-circles.
Since the formula for the circumference of a circle of 2 pie r, then in assuming that pie r is the circumference of a semi circle (2 identical quarter circles added together), what happens to the r in the formula?

6. ## Re: Calculating Distance between 2 circles

The diameter is 1, so the radius "r" is 1/2.
Just place r=1/2 into the formula.