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Intermediate Geometry : How to find the area of a sector

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

Circle

The radius of the circle above is and $\angle A=45^{\circ}$ . What is the area of the shaded section of the circle?

Possible Answers:

$8\pi$

$16\pi$

$2\pi$

$\pi$

$4\pi$

Correct answer:

$2\pi$

Explanation:

Area of Circle = πr² = π4²= 16π

Total degrees in a circle = 360

Therefore 45 degree slice = 45/360 fraction of circle = 1/8

Shaded Area = 1/8 * Total Area = 1/8 * 16π = 2π

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Example Question #31 : Circles

A circle has a diameter of meters. A certain sector of the circle has a central angle of $\small 20^\circ$ . Find the area of the sector.

Possible Answers:

$\small 6\pi\,m^2$

$\small 200\pi\,m^2$

$\small 50\pi\,m^2$

$\small 25\pi\,m^2$

$\small 30\pi\,m^2$

Correct answer:

$\small 50\pi\,m^2$

Explanation:

The formula for the area of a sector is.

$\small S=\frac{m}{360}\pi r^2$ where $\small r$ is the radius and $\small m$ is the measure of the central angle of the sector.

We are given that the diameter of the circle is 60. Therefore its radius is simply half as long, or 30.

Substituting into our equation gives

$\small \small S=\frac{20}{360}\pi(30^2)=\frac{1}{18}\pi(900)=50\pi$

Therefore our area is $\small 50\pi\,m^2$

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Example Question #32 : Circles

Find the area of a sector with a central angle of 124 degrees and a radius of .

Possible Answers:

155.82

148.20

159.22

156.29

Correct answer:

155.82

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

$\text{Area of Sector}=\frac{\text{Central Angle}}{360}\times\pi\times r^2$

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{124}{360}\times\pi\times 12^2$

Solve and round to two decimal places.

$\text{Area of Sector}=155.82$

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Example Question #33 : Circles

Find the area of a sector that has a central angle of 129 degrees and a radius of .

Possible Answers:

200.01

182.46

192.12

190.25

Correct answer:

190.25

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

$\text{Area of Sector}=\frac{\text{Central Angle}}{360}\times\pi\times r^2$

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{129}{360}\times\pi\times 13^2$

Solve and round to two decimal places.

$\text{Area of Sector}=190.25$

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Example Question #34 : Circles

Find the area of a sector that has a central angle of 130 degrees and a radius of .

Possible Answers:

412.29

409.54

485.12

399.50

Correct answer:

409.54

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

$\text{Area of Sector}=\frac{\text{Central Angle}}{360}\times\pi\times r^2$

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{130}{360}\times\pi\times 19^2$

Solve and round to two decimal places.

$\text{Area of Sector}=409.54$

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Example Question #35 : Circles

Find the area of a sector that has a central angle of 135 degrees and a radius of .

Possible Answers:

527.02

529.30

609.39

519.54

Correct answer:

519.54

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

$\text{Area of Sector}=\frac{\text{Central Angle}}{360}\times\pi\times r^2$

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{135}{360}\times\pi\times 21^2$

Solve and round to two decimal places.

$\text{Area of Sector}=519.54$

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Example Question #36 : Circles

Find the area of a sector that has a central angle of 115 degrees and a radius of .

Possible Answers:

60.39

69.21

70.05

64.23

Correct answer:

64.23

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

$\text{Area of Sector}=\frac{\text{Central Angle}}{360}\times\pi\times r^2$

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{115}{360}\times\pi\times 8^2$

Solve and round to two decimal places.

$\text{Area of Sector}=64.23$

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Example Question #37 : Circles

Find the area of a sector that has a central angle of 118 degrees and a radius of .

Possible Answers:

101.59

98.45

99.21

102.97

Correct answer:

102.97

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

$\text{Area of Sector}=\frac{\text{Central Angle}}{360}\times\pi\times r^2$

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{118}{360}\times\pi\times 10^2$

Solve and round to two decimal places.

$\text{Area of Sector}=102.97$

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Example Question #38 : Circles

Find the area of a sector that has a central angle of degrees and a radius of .

Possible Answers:

16.92

12.66

7.42

6.10

Correct answer:

7.42

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

$\text{Area of Sector}=\frac{\text{Central Angle}}{360}\times\pi\times r^2$

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{34}{360}\times\pi\times 5^2$

Solve and round to two decimal places.

$\text{Area of Sector}=7.42$

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Intermediate Geometry : How to find the area of a sector

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

Example Question #31 : Circles

Example Question #32 : Circles

Example Question #33 : Circles

Example Question #34 : Circles

Example Question #35 : Circles

Example Question #36 : Circles

Example Question #37 : Circles

Example Question #38 : Circles

All Intermediate Geometry Resources

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