ISEE Upper Level Math : Sectors

Example Questions

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Example Question #1 : How To Find The Angle For A Percentage Of A Circle

Sector TYP occupies 43% of a circle. Find the degree measure of angle TYP.

Explanation:

Sector TYP occupies 43% of a circle. Find the degree measure of angle TYP.

Use the following formula and solve for x:

Begin by dividing over the 100

Then multiply by 360

Example Question #2 : How To Find The Angle For A Percentage Of A Circle

If sector AJL covers 45% of circle J, what is the measure of sector AJL's central angle?

Explanation:

If sector AJL covers 45% of circle J, what is the measure of sector AJL's central angle?

To find an angle measure from a percentage, simply convert the percentage to a decimal and then multiply it by 360 degrees.

So, our answer is 162 degrees.

Example Question #1 : Sectors

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

Explanation:

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 #1 : How To Find The Area Of A Sector

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

Explanation:

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 #1 : How To Find The Area Of A Sector

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?

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 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

Example Question #1 : Sectors

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 #82 : Circles

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 #1 : Sectors

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 #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 length of the arc of the highlighted wedge?

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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