### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Sectors

Give the area of the white region of the above circle if has length .

**Possible Answers:**

**Correct answer:**

If we let be the circumference of the circle, then the length of is of the circumference, so

The radius is the circumference divided by :

Use the formula to find the area of the entire circle:

The area of the white region is of that of the circle, or

### Example Question #2 : Sectors

The circumference of the above circle is . Give the area of the shaded region.

**Possible Answers:**

**Correct answer:**

The radius of a circle is found by dividing the circumference by :

The area of the entire circle can be found by substituting for in the formula:

.

The area of the shaded sector is of the total area:

### Example Question #3 : Sectors

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the area of the highlighted wedge?

**Possible Answers:**

**Correct answer:**

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the area of the highlighted wedge?

To begin, let's recall our formula for area of a sector.

Now, we have theta and r, so we just need to plug them in and simplify!

So our answer is

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