### All GRE Math Resources

## Example Questions

### Example Question #1 : How To Find The Length Of An Arc

What is the perimeter of a pie piece if the pie is sliced into 40 degree pieces and its area is 361π?

**Possible Answers:**

38π/9

38 + 38π/9

40.1π

2.1

38π

**Correct answer:**

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 πr^{2} = 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 #31 : Plane Geometry

What is the length of the arc of a circle with radius 10 that traces a 50 degree angle?

**Possible Answers:**

25*π*/9

25*π*/7

25*π*/29

25*π*

20*π*/9

**Correct answer:**

25*π*/9

length of an arc = (degrees * 2*πr)*/360 = (50 * 2*π ** 10)/360 = 25*π*/9

### Example Question #32 : Circles

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 and equally-sized pieces.

Quantity B: The distance covered by the ant when walking over a complete personal pizza with a diameter of inches.

What can we say about the two quantities?

**Possible Answers:**

Quantity A is larger.

Quantity B is larger.

The two quantities are equal.

The relationship between the two quantities cannot be determined.

**Correct answer:**

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 , or , of the pizza.

Now, we know the circumference of a circle is or

For our example, let's use the latter. Since , we know:

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 . Thus, we know that Quantity B is larger than Quantity A.

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