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

Study concepts, example questions & explanations for ISEE Upper Level Math

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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:

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 : 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:

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 #1 : How To Find The Length Of An Arc

Inscribed

In the above figure, express  in terms of .

Possible Answers:

Correct answer:

Explanation:

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

Intercepted

In the above diagram, radius .

Give the length of .

Possible Answers:

Correct answer:

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 #2 : 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:

Explanation:

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

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