### All ISEE Upper Level Math Resources

## Example Questions

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

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

**Possible Answers:**

**Correct answer:**

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is feet. One hour and twenty minutes is hours, so the tip of the hand moved feet, or inches.

### Example Question #2 : How To Find The Length Of An Arc

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

**Possible Answers:**

It is impossible to tell from the information given

**Correct answer:**

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is feet. minutes is one-third of an hour, so the tip of the minute hand moves feet, or inches.

### Example Question #3 : How To Find The Length Of An Arc

In the above figure, express in terms of .

**Possible Answers:**

**Correct answer:**

The measure of an arc - - intercepted by an inscribed angle - - is twice the measure of that angle, so

### Example Question #4 : How To Find The Length Of An Arc

In the above diagram, radius .

Give the length of .

**Possible Answers:**

**Correct answer:**

The circumference of a circle is multiplied by its radius , so

.

, being an inscribed angle of the circle, intercepts an arc with twice its measure:

The length of is the circumference multiplied by :

.

### Example Question #5 : How To Find The Length Of An Arc

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 length of the arc 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 length of the arc of the highlighted wedge?

To begin, let's recall our formula for length of an arc.

Now, just plug in and simplify

So, our answer is 4.54in