IXL - Area of sectors (Geometry practice)

The radius of a circle is 6 inches. What is the area of a sector bounded by a 45° arc?

45°

Give the exact answer in simplest form.

square inches

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Learn with an example

question

The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 90° arc?

90°

Give the exact answer in simplest form.

square kilometers

key idea

The formula for the area of a sector is

360

where

is the area of the sector,

is the area of the circle, and

is the measure in degrees of the arc bounding the sector.

solution

The sector's area depends on the arc's measure and the circle's area. You already know that the arc's measure is 90°, so find the circle's area.

First, find the area of the circle.

Plug in

Square

The area of the circle is

square kilometers.

Now, find the area of the sector.

360

Plug in

and

360

Plug in

and

Multiply and simplify

The area of the sector is

square kilometers.

Looking for more? Try these:

Lesson: Area of sectors

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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: Area of sectors

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