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Intermediate Geometry : Circles

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #21 : How To Find The Area Of A Sector

Find the area of the sector if it has a central angle of 107 degrees and a radius of .

Possible Answers:

449.02

411.78

395.52

403.20

Correct answer:

411.78

Explanation:

The circle in question can be drawn as shown by the figure below:

Since the area of a sector is just a fractional part of the area of a circle, we can write the following equation to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Central angle}}{360}\pi r^2$ , where is the radius of the circle.

Plug in the given central angle and radius to find the area of the sector.

$\text{Area of Sector}=\frac{107}{360}\pi(21)^2=411.78$

Make sure to round to two places after the decimal.

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Example Question #51 : Sectors

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

Possible Answers:

1.54

1.33

1.49

1.02

Correct answer:

1.02

Explanation:

The circle in question can be drawn as shown by the figure below:

Since the area of a sector is just a fractional part of the area of a circle, we can write the following equation to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Central angle}}{360}\pi r^2$ , where is the radius of the circle.

Plug in the given central angle and radius to find the area of the sector.

$\text{Area of Sector}=\frac{13}{360}\pi(3)^2=1.02$

Make sure to round to two places after the decimal.

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Example Question #51 : Circles

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

Possible Answers:

3.30

3.29

4.81

2.71

Correct answer:

3.30

Explanation:

The circle in question can be drawn as shown by the figure below:

Since the area of a sector is just a fractional part of the area of a circle, we can write the following equation to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Central angle}}{360}\pi r^2$ , where is the radius of the circle.

Plug in the given central angle and radius to find the area of the sector.

$\text{Area of Sector}=\frac{42}{360}\pi(3)^2=3.30$

Make sure to round to two places after the decimal.

Report an Error

Example Question #22 : How To Find The Area Of A Sector

Find the area of the sector if it has a central angle of 164 degrees and a radius of .

Possible Answers:

114.12

102.44

91.59

105.69

Correct answer:

91.59

Explanation:

The circle in question can be drawn as shown by the figure below:

Since the area of a sector is just a fractional part of the area of a circle, we can write the following equation to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Central angle}}{360}\pi r^2$ , where is the radius of the circle.

Plug in the given central angle and radius to find the area of the sector.

$\text{Area of Sector}=\frac{164}{360}\pi(8)^2=91.59$

Make sure to round to two places after the decimal.

Report an Error

Example Question #23 : How To Find The Area Of A Sector

Find the area of a sector if it has a central angle of 134 degrees and a radius of .

Possible Answers:

310.21

337.95

394.89

456.42

Correct answer:

337.95

Explanation:

The circle in question can be drawn as shown by the figure below:

Since the area of a sector is just a fractional part of the area of a circle, we can write the following equation to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Central angle}}{360}\pi r^2$ , where is the radius of the circle.

Plug in the given central angle and radius to find the area of the sector.

$\text{Area of Sector}=\frac{134}{360}\pi(17)^2=337.95$

Make sure to round to two places after the decimal.

Report an Error

Example Question #21 : How To Find The Area Of A Sector

Find the area of a sector that has a central angle of 300 degrees and a radius of .

Possible Answers:

490.05

513.13

551.29

601.48

Correct answer:

513.13

Explanation:

The circle in question can be drawn as shown by the figure below:

Since the area of a sector is just a fractional part of the area of a circle, we can write the following equation to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Central angle}}{360}\pi r^2$ , where is the radius of the circle.

Plug in the given central angle and radius to find the area of the sector.

$\text{Area of Sector}=\frac{300}{360}\pi(14)^2=513.13$

Make sure to round to two places after the decimal.

Report an Error

Example Question #28 : How To Find The Area Of A Sector

Find the area of a sector if it has an arc length of and a radius of .

Possible Answers:

The area of the sector cannot be determined.

$\frac{5}{2}$

$\frac{3}{2}$

$\frac{7}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{3(1)}{2}=\frac{3}{2}$

Report an Error

Example Question #52 : Sectors

Find the area of a sector if it has an arc length of and a radius of .

Possible Answers:

$\frac{55}{2}\pi$

$52\pi$

Correct answer:

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{14(8)}{2}=56$

Report an Error

Example Question #53 : Circles

Find the area of a sector if it has an arc length of $2\pi$ and a radius of .

Possible Answers:

19.02

17.61

20.31

18.85

Correct answer:

18.85

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{2\pi(6)}{2}=18.85$

Make sure to round to places after the decimal.

Report an Error

Example Question #31 : How To Find The Area Of A Sector

Find the area of a sector if it has an arc length of $9\pi$ and a radius of .

Possible Answers:

141.37

155.30

195.67

139.95

Correct answer:

141.37

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{9\pi(10)}{2}=141.37$

Make sure to round to places after the decimal.

Report an Error

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Intermediate Geometry : Circles

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #21 : How To Find The Area Of A Sector

Example Question #51 : Sectors

Example Question #51 : Circles

Example Question #22 : How To Find The Area Of A Sector

Example Question #23 : How To Find The Area Of A Sector

Example Question #21 : How To Find The Area Of A Sector

Example Question #28 : How To Find The Area Of A Sector

Example Question #52 : Sectors

Example Question #53 : Circles

Example Question #31 : How To Find The Area Of A Sector

All Intermediate Geometry Resources

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