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Intermediate Geometry : How to find the length of an arc

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Example Questions

Example Question #91 : Sectors

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:

$10\pi$

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

$9\pi$

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

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 #92 : Sectors

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:

$68\pi$

$72\pi$

$70\pi$

$66\pi$

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.

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

Report an Error

Example Question #93 : Sectors

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:

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

$13\pi$

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

$12\pi$

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 #94 : Sectors

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:

$20\pi$

$18\pi$

$12\pi$

$16\pi$

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 #95 : Sectors

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:

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

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

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

$20\pi$

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 #96 : Sectors

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:

$17\pi$

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

$16\pi$

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

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 #97 : Sectors

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:

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

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

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

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

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 #91 : Sectors

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:

$29\pi$

$28\pi$

$30\pi$

$31\pi$

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 #99 : Sectors

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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Intermediate Geometry : How to find the length of an arc

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #91 : Sectors

Example Question #92 : Sectors

Example Question #93 : Sectors

Example Question #94 : Sectors

Example Question #95 : Sectors

Example Question #96 : Sectors

Example Question #97 : Sectors

Example Question #91 : Sectors

Example Question #99 : Sectors

All Intermediate Geometry Resources

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