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Intermediate Geometry : How to find the length of an arc

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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:

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

$9\pi$

$10\pi$

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

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 #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:

$68\pi$

$70\pi$

$72\pi$

$66\pi$

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 #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:

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

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

$12\pi$

$13\pi$

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 #91 : Intermediate Geometry

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:

$20\pi$

$12\pi$

$18\pi$

$16\pi$

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 #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:

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

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

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

$20\pi$

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 #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:

$17\pi$

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

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

$16\pi$

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:

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

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

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

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

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:

$30\pi$

$28\pi$

$29\pi$

$31\pi$

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 #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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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 #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 #91 : Intermediate Geometry

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

All Intermediate Geometry Resources

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