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Intermediate Geometry : Sectors

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #21 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is and the measurement of the central angle is 100 degrees.

Possible Answers:

$\frac{85}{9}\pi$

$\frac{80}{9}\pi$

$9\pi$

$10\pi$

Correct answer:

$\frac{80}{9}\pi$

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

$\text{Length of Arc}=\frac{\text{Measure of central angle}}{360}\times2\pi\times \text{radius}$

Substitute in the given values for the central angle and the radius.

$\text{Length of Arc}=\frac{100}{360}\times 2\pi \times 16$

Solve.

$\text{Length of Arc}=\frac{80}{9}\pi$

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Example Question #22 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is and the measurement of the central angle is 120 degrees.

Possible Answers:

$68\pi$

$66\pi$

$72\pi$

$70\pi$

Correct answer:

$68\pi$

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

$\text{Length of Arc}=\frac{\text{Measure of central angle}}{360}\times2\pi\times \text{radius}$

Substitute in the given values for the central angle and the radius.

$\text{Length of Arc}=\frac{120}{360}\times 2\pi \times 17$

Solve.

$\text{Length of Arc}=68\pi$

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Example Question #23 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is and the measurement of the central angle is 125 degrees.

Possible Answers:

$\frac{27}{2}\pi$

$13\pi$

$\frac{25}{2}\pi$

$12\pi$

Correct answer:

$\frac{25}{2}\pi$

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

$\text{Length of Arc}=\frac{\text{Measure of central angle}}{360}\times2\pi\times \text{radius}$

Substitute in the given values for the central angle and the radius.

$\text{Length of Arc}=\frac{125}{360}\times 2\pi \times 18$

Solve.

$\text{Length of Arc}=\frac{25}{2}\pi$

Report an Error

Example Question #24 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is and the measurement of the central angle is 160 degrees.

Possible Answers:

$16\pi$

$12\pi$

$18\pi$

$20\pi$

Correct answer:

$16\pi$

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

$\text{Length of Arc}=\frac{\text{Measure of central angle}}{360}\times2\pi\times \text{radius}$

Substitute in the given values for the central angle and the radius.

$\text{Length of Arc}=\frac{160}{360}\times 2\pi \times 18$

Solve.

$\text{Length of Arc}=16\pi$

Report an Error

Example Question #25 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is and the measurement of the central angle is 170 degrees.

Possible Answers:

$20\pi$

$\frac{185}{9}\pi$

$\frac{175}{9}\pi$

$\frac{170}{9}\pi$

Correct answer:

$\frac{170}{9}\pi$

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

$\text{Length of Arc}=\frac{\text{Measure of central angle}}{360}\times2\pi\times \text{radius}$

Substitute in the given values for the central angle and the radius.

$\text{Length of Arc}=\frac{170}{360}\times 2\pi \times 20$

Solve.

$\text{Length of Arc}=\frac{170}{9}\pi$

Report an Error

Example Question #26 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is and the measurement of the central angle is 140 degrees.

Possible Answers:

$\frac{52}{3}\pi$

$\frac{49}{3}\pi$

$17\pi$

$16\pi$

Correct answer:

$\frac{49}{3}\pi$

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

$\text{Length of Arc}=\frac{\text{Measure of central angle}}{360}\times2\pi\times \text{radius}$

Substitute in the given values for the central angle and the radius.

$\text{Length of Arc}=\frac{140}{360}\times 2\pi \times 21$

Solve.

$\text{Length of Arc}=\frac{49}{3}\pi$

Report an Error

Example Question #27 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is and the measurement of the central angle is 200 degrees.

Possible Answers:

$\frac{220}{9}\pi$

$\frac{229}{9}\pi$

$\frac{211}{9}\pi$

$\frac{238}{9}\pi$

Correct answer:

$\frac{220}{9}\pi$

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

$\text{Length of Arc}=\frac{\text{Measure of central angle}}{360}\times2\pi\times \text{radius}$

Substitute in the given values for the central angle and the radius.

$\text{Length of Arc}=\frac{200}{360}\times 2\pi \times 22$

Solve.

$\text{Length of Arc}=\frac{220}{9}\pi$

Report an Error

Example Question #28 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is and the measurement of the central angle is 210 degrees.

Possible Answers:

$31\pi$

$28\pi$

$29\pi$

$30\pi$

Correct answer:

$28\pi$

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

$\text{Length of Arc}=\frac{\text{Measure of central angle}}{360}\times2\pi\times \text{radius}$

Substitute in the given values for the central angle and the radius.

$\text{Length of Arc}=\frac{210}{360}\times 2\pi \times 24$

Solve.

$\text{Length of Arc}=28\pi$

Report an Error

Example Question #29 : How To Find The Length Of An Arc

In the figure below, $\text{chord AB}\parallel\text{chord CD}$ . If $\text{Arc AC}$ is degrees, in degrees, what is the measure of $\text{Arc BD}$ ?

Possible Answers:

The measurement of $\text{Arc BD}$ cannot be determined with the information given.

Correct answer:

Explanation:

Recall that when chords are parallel, the arcs that are intercepted are congruent. Thus, $\text{Arc AC}=\text{Arc BD}$ .

Then, $\text{Arc BD}$ must also be degrees.

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

Circle

In the circle above, the length of arc BC is 100 degrees, and the segment AC is a diameter. What is the measure of angle ADB in degrees?

Possible Answers:

100

cannot be determined

Correct answer:

Explanation:

Since we know that segment AC is a diameter, this means that the length of the arc ABC must be 180 degrees. This means that the length of the arc AB must be 80 degrees.

Since angle ADB is an inscribed angle, its measure is equal to half of the measure of the angle of the arc that it intercepts. This means that the measure of the angle is half of 80 degrees, or 40 degrees.

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Intermediate Geometry : Sectors

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #21 : How To Find The Length Of An Arc

Example Question #22 : How To Find The Length Of An Arc

Example Question #23 : How To Find The Length Of An Arc

Example Question #24 : How To Find The Length Of An Arc

Example Question #25 : How To Find The Length Of An Arc

Example Question #26 : How To Find The Length Of An Arc

Example Question #27 : How To Find The Length Of An Arc

Example Question #28 : How To Find The Length Of An Arc

Example Question #29 : How To Find The Length Of An Arc

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

All Intermediate Geometry Resources

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