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Intermediate Geometry : Sectors

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Example Question #7 : How To Find The Percentage Of A Sector From An Angle

A survey was given to 300 local townspeople regarding their favorite local dish. The results of the survey are below, with the number of degrees of each sector representing each dish following.

Fried chicken, 87 degrees

Steak and potatoes, 75 degrees

Corned beef hash, 82 degrees

Chicken enchiladas, 94 degrees

Bison burger, 22 degrees

What percent of the local townspeople prefer a dish that includes chicken?

Possible Answers:

$24.2\%$

$50.3\%$

$26.1\%$

$181\%$

$5\%$

Correct answer:

$50.3\%$

Explanation:

First add together the number of degrees of both sectors representing a dish with chicken (fried chicken and chicken enchiladas), 87 + 94.

Then set-up a proportion with this sum:

$\frac{181}{360} = \frac{x}{100}$ and solve for .

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Example Question #1 : How To Find The Percentage Of A Sector From An Angle

A pie chart represents the ages of children in a local basketball league. The data is shown below, with the age range of each sector followed by the number of degrees of that sector.

Ages 2-4, 20 degrees

Ages 5-7, 30 degrees

Ages 8-10, 100 degrees

Ages 11-13, 90 degrees

Ages 14-16, ? degrees

What percent of the children in the basketball league are between the ages of 14-16?

Possible Answers:

$3.3\%$

$33.3\%$

$66.7\%$

$120\%$

None of the other answers.

Correct answer:

$33.3\%$

Explanation:

First add together the degrees of the sectors representing children ages 2-13. Then take that sum, 240 degrees, away from the total degrees of the circle, 360 degrees.

Finally set-up a proportion with the remaining degrees (120) which represents the sector of children ages 14-16.

Solve your proportion:

$\frac{120}{360} = \frac{x}{100}$ .

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Example Question #9 : How To Find The Percentage Of A Sector From An Angle

A circle chart represents the survey results of the following question:

How many hours a week do you typically spend watching TV?

The results are below, with the sector title and the number of degrees of each sector following.

Less than 1 hour, 40 degrees

1-4 hours, 45 degrees

5-8 hours, 30 degrees

9-12 hours, 100 degrees

13-16 hours, 85 degrees

17 hours or more, 60 degrees

What percent of people surveyed watch TV for 9 or more hours a week?

Possible Answers:

$245\%$

$51.4\%$

$27.8\%$

$68.1\%$

$6.8\%$

Correct answer:

$68.1\%$

Explanation:

First, add together the degrees from the 3 sectors that include 9 or more hours of TV: 100 degrees, 85 degrees and 60 degrees.

Take this sum, 245 degrees, and set-up a proportion:

$\frac{245}{360} = \frac{x}{100}$ and solve for .

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Example Question #1 : How To Find The Percentage Of A Sector From An Angle

A circle graph represents the demographics of a major US city. The data is shown below with the category followed by the number of degrees making up that category's sector.

Black or African-American: 100 degrees

Hispanic or Latino: 100 degrees

White: 80 degrees

Two or more races: ? degrees

What percent of the city's population classifies themselves as being 2 or more races?

Possible Answers:

$22.2\%$

$44.4\%$

$2.2\%$

$80\%$

$27.8\%$

Correct answer:

$22.2\%$

Explanation:

First, add together the degrees of the known sectors: 100 degrees, 100 degrees, and 80 degrees.

Subtract this sum (280 degrees) from the total number of degrees in a circle (360 degrees).

Take this difference to set-up a proportion:

$\frac{80}{360} = \frac{x}{100}$ and solve for .

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Example Question #11 : How To Find The Percentage Of A Sector From An Angle

A survey was given to 1,000 middle school students across the United States, asking them to choose their favorite subject in school. The results of the survey are below, with each subject followed by the number of degrees composing that subject's sector in the circle graph displaying this data.

Math, 75 degrees

English, 58 degrees

Science, 62 degrees

Social Studies, 100 degrees

Music, Art or PE: 65 degrees

What percent of students prefer a subject that is not Music, Art or PE?

Possible Answers:

$8.2\%$

$81.9\%$

$18.1\%$

$295\%$

None of the other answers.

Correct answer:

$81.9\%$

Explanation:

First, add together the degrees of the sectors representing Math, English, Science and Social Studies.

Take this sum, 295 and set-up a proportion:

$\frac{295}{360} = \frac{x}{100}$ and solve for .

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Example Question #22 : Intermediate Geometry

Reference a map of major cities on the West Coast to help you with this question!

A survey was given to fans throughout the West Coast, asking them who their favorite team was. The results are below with the team name and the degrees making up the sector representing that team in a circle graph that displayed this data.

Team A: 123 degrees

Team B: 89 degrees

Team C: 36 degrees

Team D: 20 degrees

Other: 92 degrees

What percent of fans prefere Team A, C, or D?

Possible Answers:

$25.6\%$

$5\%$

$34.2\%$

$39.7\%$

$49.7\%$

Correct answer:

$49.7\%$

Explanation:

First add together the degrees from the sectors representing Teams A, C, and D.

Take this sum, 179 and set-up a proportion:

$\frac{179}{360} = \frac{x}{100}$ and solve for .

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Example Question #23 : Intermediate Geometry

A pie chart depicts the favorite beverages of high schoolers. Below is the data with the beverage and the number of degrees making up that beverage's sector.

Soda: 86 degrees

Diet Soda: 44 degrees

Water: 55 degrees

Juice: 99 degrees

Lemonade: 66 degrees

Other: ? degrees

What percent of high schoolers prefer a beverage that was not specifically listed as a choice?

Possible Answers:

$27.8\%$

None of the other answers.

$2.8\%$

$10\%$

$97.2\%$

Correct answer:

$2.8\%$

Explanation:

First add together the known sectors. Use that sum (350 degrees) and subtract from the total number of degrees in a circle (360 degrees).

Take that difference and set-up a proportion:

$\frac{10}{360} = \frac{x}{100}$ and solve for .

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Example Question #11 : How To Find The Percentage Of A Sector From An Angle

A circle graph displays data of the eye colors of a group of middle schoolers. The data is shown below with the eye color followed by the number of degrees composing that sector.

Brown: 208 degrees

Green: 20 degrees

Blue: 25 degrees

Hazel: 50 degrees

Other: 57 degrees

What percent of students have brown eyes?

Possible Answers:

None of the other answers.

$5.8\%$

$78.3\%$

$208\%$

$57.8\%$

Correct answer:

$57.8\%$

Explanation:

Take the degrees representing the brown eye sector and set-up a proportion:

$\frac{208}{360} = \frac{x}{100}$ and solve for .

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Example Question #25 : Intermediate Geometry

Circle 1

In the above diagram, $\bigtriangleup ABO$ is an equilateral triangle. What percent of the circle has been shaded in?

Possible Answers:

$83\frac{1}{3} \%$

$90 \%$

$75 \%$

$87 \frac{1}{2} \%$

$80 \%$

Correct answer:

$83\frac{1}{3} \%$

Explanation:

The three interior angles of equilateral triangle $\bigtriangleup ABO$ - in particular, $\angle AOB$ - measure $60^{\circ }$ . This makes the unshaded sector of the circle a sector with a $60^{\circ }$ central angle, or, equivalently, a $60^{\circ }$ sector. The shaded sector is therefore one of measure $(360 - 60)^{\circ } = 300^{\circ }$ . It is therefore

$\frac{300^{\circ }}{360^{\circ }} \times 100 \% = \frac{5}{6} \times 100 \% = 83 \frac{1}{3} \%$

of the circle.

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Example Question #1 : How To Find The Area Of A Sector

Find the approximate area of the shaded portion of the figure.

Circle1

Possible Answers:

$3200\ cm^{2}$

$3900\ cm^{2}$

$7100\ cm^{2}$

$4200\ cm^{2}$

$6200\ cm^{2}$

Correct answer:

$6200\ cm^{2}$

Explanation:

The answer is approximately $6200\ cm^{2}$ .

First, you would need to find the diameter of the circle. Use the Pythagorean Theorem to get

$50^{2}+120^{2}=130^{2}$

$78^{2}+104^{2}=130^{2}$

Since the diameter is 130, we divide by 2 to get 65 cm for our radius. Then the area of the circle is

$\pi r^{2} = \pi \cdot 65^{2} \approx 13,273 \ cm^{2}$

Next we would find the area of each triangle:

$\frac{1}{2} (50)(120) = 3000cm^{2}$

and

$\frac{1}{2} (78)(104) = 4056cm^{2}$

Then we would subtract these from our answer above to get:

$13273-3000 - 4056 \approx 6200\ cm^{2}$ .

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Intermediate Geometry : Sectors

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #7 : How To Find The Percentage Of A Sector From An Angle

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

Example Question #9 : How To Find The Percentage Of A Sector From An Angle

Example Question #1 : How To Find The Percentage Of A Sector From An Angle

Example Question #11 : How To Find The Percentage Of A Sector From An Angle

Example Question #22 : Intermediate Geometry

Example Question #23 : Intermediate Geometry

Example Question #11 : How To Find The Percentage Of A Sector From An Angle

Example Question #25 : Intermediate Geometry

Example Question #1 : How To Find The Area Of A Sector

All Intermediate Geometry Resources

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