Geometry - 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 $\text{Arc BD}$ ?

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

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.

Find the length of the arc if the radius of a circle is and the measure of the central angle is degrees.

$\frac{11}{3}\pi$

$4\pi$

$\frac{13}{3}\pi$

$5\pi$

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.

$\text{Length of Arc}=\frac{55}{360}\times 2\pi \times 12$

Solve.

$\text{Length of Arc}=\frac{11}{3}\pi$

Find the perimeter around the following semicircle.

Semicirc

$9\pi +18\ cm$

$9\pi \ cm$

$18\pi \ cm$

$27\pi \ cm$

$18\pi +18\ cm$

Explanation

The answer is $9\pi + 18cm$ .

First, you would need to find the radius of the semi-circle. 18 divided by 2 results in 9 cm for the radius. Then you would take the formula for finding circumference $C=2\pi r$ and plug in to get

$C=18\pi$ .

Then you would divide that result by 2 to get $9\pi$ since it is a semicircle. Lastly you would add 18 cm to $9\pi$ because the perimeter is the sum of the semicircle and the diameter. Remember that they are not like terms.

If you chose $9\pi$ , you forgot to include the diameter.

If you chose $27\pi$ , you added and , but they are not like terms.

If you chose $18\pi + 18$ , remember that you only need half of the circumference.

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

$\frac{169}{36}\pi$

$\frac{19}{4}\pi$

$\frac{37}{6}\pi$

$\frac{110}{7}\pi$

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.

$\text{Length of Arc}=\frac{65}{360}\times 2\pi \times 13$

Solve.

$\text{Length of Arc}=\frac{169}{36}\pi$

The radius of a circle is . Find the length of an arc if it has a measurement of degrees.

$4\pi$

$2\pi$

$6\pi$

$8\pi$

Explanation

Recall that the length of an arc is merely a part of the circle's circumference.

We can then write the following equation to find the length of an arc:

$\text{Arc Length}=\frac{\text{Arc angle measure}}{360}\times2\pi\times \text{radius}$

Plug in the values of the arc angle measure and the radius to find the length of the arc.

$\text{Arc Length}=\frac{240}{360}\times 2\pi\times 3=4\pi$

If the area of a circle is 1.44 $\pi$ , what is its circumference?

$2.4\pi$

$1.2\pi$

$1.44\pi$

$2.88\pi$

$7.54\pi$

Explanation

The answer is $2.4 \pi$ .

Utilizing the formula for area of a circle $\left( \pi r^{2}\right)$ , you would plug in the answer for area as

$1.44\pi$ = $\pi r^{2}$

Divide both sides by $\pi$ .

Then square root both sides to get

Then plug in 1.2 for in the equation for circumference for a circle, $2\pi r$ . Thus

$C = 2.4\pi$

The radius of a circle is . Find the length of an arc that has a measurement of degrees.

$\pi$

$\frac{1}{2}\pi$

$2\pi$

$\frac{1}{4}\pi$

Explanation

Recall that the length of an arc is merely a part of the circle's circumference.

We can then write the following equation to find the length of an arc:

$\text{Arc Length}=\frac{\text{Arc angle measure}}{360}\times2\pi\times \text{radius}$

Plug in the values of the arc angle measure and the radius to find the length of the arc.

$\text{Arc Length}=\frac{45}{360}\times 2\pi\times 4=\pi$

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

$\frac{35}{6}\pi$

$\frac{13}{3}\pi$

$\frac{25}{6}\pi$

$8\pi$

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.

$\text{Length of Arc}=\frac{75}{360}\times 2\pi \times 14$

Solve.

$\text{Length of Arc}=\frac{35}{6}\pi$

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

$\frac{20}{3}\pi$

$6\pi$

$\frac{22}{3}\pi$

$\frac{29}{3}\pi$

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.

$\text{Length of Arc}=\frac{80}{360}\times 2\pi \times 15$

Solve.

$\text{Length of Arc}=\frac{20}{3}\pi$

The radius of a circle is . Find the length of an arc if it has a measure of degrees.

$\frac{25}{6}\pi$

$4\pi$

$\frac{9}{2}\pi$

$\frac{10}{3}\pi$

Explanation

Recall that the length of an arc is merely a part of the circle's circumference.

We can then write the following equation to find the length of an arc:

$\text{Arc Length}=\frac{\text{Arc angle measure}}{360}\times2\pi\times \text{radius}$

Plug in the values of the arc angle measure and the radius to find the length of the arc.

$\text{Arc Length}=\frac{150}{360}\times 2\pi\times 5=\frac{25}{6}\pi$

How to find the length of an arc

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