IXL - Arc length (Geometry practice)

The radius of a circle is 2 inches. What is the length of a 90° arc?

90°

Give the exact answer in simplest form.

inches

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Learn with an example

question

The radius of a circle is 1 meter. What is the length of a 135° arc?

135°

Give the exact answer in simplest form.

meters

key idea

The formula for the length of an arc is

360

where

is the arc length,

is the circumference, and

is the measure of the arc in degrees.

solution

The arc's length depends on the arc's measure and the circle's circumference. You already know that the arc's measure is 135°, so find the circle's circumference.

First, find the circumference.

Plug in

(

)

Plug in

Multiply

The circumference is

meters.

Now, find the length of the arc.

360

Plug in

and

135

360

Plug in

and

135

Multiply and simplify

The length of the arc is

meters.

Looking for more? Try these:

Lesson: Arc length

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Teacher tools

Work it out

Not feeling ready yet? These can help:

W.3Understand arc length and sector area of a circle

S.9Area and circumference of circles

W.2Central angles and arc measures

Lesson: Arc length

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