# ISEE Upper Level Math : How to find the length of an arc

## 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?

Explanation:

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 : Sectors

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

It is impossible to tell from the information given

Explanation:

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 : Sectors

In the above figure, express  in terms of .

Explanation:

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

### Example Question #81 : Circles

In the above diagram, radius .

Give the length of .

Explanation:

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 : 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 length of the arc of the highlighted wedge?