GRE Math : How to find the length of an arc
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Example Questions
Example Question #31 : Geometry
What is the perimeter of a pie piece if the pie is sliced into 40 degree pieces and its area is 361π?
2.1
38 + 38π/9
38π/9
38π
40.1π
38 + 38π/9
The perimeter of a given pie-piece will be equal to 2 radii plus the outer arc (which is a percentage of the circumference). For our piece, this arc will be 40/360 or 1/9 of the circumference. If the area is 361π, this means πr2 = 361 and that the radius is 19. The total circumference is therefore 2 * 19 * π or 38π.
The total perimeter of the pie piece is therefore 2 * r + (1 / 9) * c = 2 * 19 + (1/9) * 38π = 38 + 38π/9
Example Question #2 : How To Find The Length Of An Arc
What is the length of the arc of a circle with radius 10 that traces a 50 degree angle?
25π
25π/29
20π/9
25π/9
25π/7
25π/9
length of an arc = (degrees * 2πr)/360 = (50 * 2π * 10)/360 = 25π/9
Example Question #1 : How To Find The Length Of An Arc
An ant walks around the edge of circular pizzas left on the counter of a pizza shop. On most days, it is shaken off the pizza before it manages to walk the complete distance.
Quantity A: The distance covered by the ant when walking over four slices of a pizza with a diameter of 
Quantity B: The distance covered by the ant when walking over a complete personal pizza with a diameter of 
What can we say about the two quantities?
The relationship between the two quantities cannot be determined.
Quantity B is larger.
The two quantities are equal.
Quantity A is larger.
Quantity B is larger.
Let's compute each quantity.
Quantity A
This is a little bit more difficult than quantity B. It requires us to compute an arc length, for the ant does not walk around the whole pizza; however, this is not very hard. What we know is that the ant walks around 
Now, we know the circumference of a circle is 
For our example, let's use the latter. Since 
However, our ant walks around only part of this, namely:
Quantity B
This is really just a matter of computing the circumference of the circle. For our value, we know this to be:
Now, we can compare these by taking quantity A and reducing the fraction to be 
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