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Intermediate Geometry : Circles

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #11 : How To Find The Area Of A Sector

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

Possible Answers:

68.72

72.56

69.01

77.82

Correct answer:

68.72

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.

$\text{Area of Sector}=\frac{35}{360}\times\pi\times 15^2$

Solve and round to two decimal places.

$\text{Area of Sector}=68.72$

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Example Question #12 : How To Find The Area Of A Sector

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

Possible Answers:

98.20

115.39

110.09

112.91

Correct answer:

110.09

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.

$\text{Area of Sector}=\frac{15}{360}\times\pi\times 29^2$

Solve and round to two decimal places.

$\text{Area of Sector}=110.09$

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Example Question #13 : How To Find The Area Of A Sector

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

Possible Answers:

2.98

5.19

6.72

3.14

Correct answer:

3.14

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.

$\text{Area of Sector}=\frac{40}{360}\times\pi\times 3^2$

Solve and round to two decimal places.

$\text{Area of Sector}=3.14$

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Example Question #14 : How To Find The Area Of A Sector

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

Possible Answers:

12.48

11.09

8.60

10.37

Correct answer:

10.37

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.

$\text{Area of Sector}=\frac{33}{360}\times\pi\times 6^2$

Solve and round to two decimal places.

$\text{Area of Sector}=10.37$

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Example Question #41 : Plane Geometry

If the sector in the provided illustration has an angle of $37.5^{\circ}$ and the circle has a radius of $4.2\;cm$ , what is the area of the sector? Round to the nearest tenth.

Varsity geometry

Possible Answers:

$4.3\;cm^2$

$8.7\;cm^2$

$6.2\;cm^2$

$7.2\;cm^2$

$5.8\;cm^2$

Correct answer:

$5.8\;cm^2$

Explanation:

To solve for the area of the sector, it helps to solve for the area of the complete circle and multiple that value by the sector angle over the full $360^{\circ}$ of a complete circle:

$\\Sector\;Area=\pi\cdot(4.2\;cm)^2\cdot\frac{37.5^{\circ}}{360^{\circ}}\\Sector\;Area=55.42\;cm^2\cdot\frac{37.5^{\circ}}{360^{\circ}}\approx5.8\;cm^2$

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Example Question #16 : How To Find The Area Of A Sector

Find the area of the sector that has a central angle of 160 degrees and a radius of .

Possible Answers:

201.06

197.55

188.04

149.24

Correct answer:

201.06

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.

$\text{Area of Sector}=\frac{160}{360}\pi(12)^2=201.06$

Make sure to round to two places after the decimal.

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Example Question #17 : How To Find The Area Of A Sector

Find the area of a sector that has a central angle of 260 degrees and a radius of .

Possible Answers:

49.09

53.51

50.08

56.72

Correct answer:

56.72

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.

$\text{Area of Sector}=\frac{260}{360}\pi(5)^2=56.72$

Make sure to round to two places after the decimal.

Report an Error

Example Question #18 : How To Find The Area Of A Sector

Find the area of a sector that has a central angle of 170 degrees and a radius of .

Possible Answers:

13.35

14.49

12.09

10.08

Correct answer:

13.35

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.

$\text{Area of Sector}=\frac{170}{360}\pi(3)^2=13.35$

Make sure to round to two places after the decimal.

Report an Error

Example Question #19 : How To Find The Area Of A Sector

Find the area of a sector if it has a central angle of 250 degrees and a radius of .

Possible Answers:

223.31

290.68

209.49

218.17

Correct answer:

218.17

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.

$\text{Area of Sector}=\frac{250}{360}\pi(10)^2=218.17$

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 if it has a central angle of degrees and a radius of .

Possible Answers:

11.92

9.35

8.04

10.02

Correct answer:

9.35

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.

$\text{Area of Sector}=\frac{67}{360}\pi(4)^2=9.35$

Make sure to round to two 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 #11 : How To Find The Area Of A Sector

Example Question #12 : How To Find The Area Of A Sector

Example Question #13 : How To Find The Area Of A Sector

Example Question #14 : How To Find The Area Of A Sector

Example Question #41 : Plane Geometry

Example Question #16 : How To Find The Area Of A Sector

Example Question #17 : How To Find The Area Of A Sector

Example Question #18 : How To Find The Area Of A Sector

Example Question #19 : How To Find The Area Of A Sector

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

All Intermediate Geometry Resources

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