Area of Sector - Degrees

Area of Sector - Degrees - How it Works - Video

Example 1

Example 1:

To find the area of the sector of a circle we need the radius and the central angle. Then we can use the formula, Area = πr²* θ/360°. Now our first step is substitute the radius and the central into the formula.

So we have Area of the Shaded Sector AB = π(4)² * (60°)/360°.

Next we square the number, 4, next to pi ==> 16π * (60°)/360°.

Now we simplify the 60 and the 360 by dividing each number by 60° ==> 16π * 1/6.

Next we simplify the two numbers 16 and 6 by dividing each number by 2 ==> 8*1/3*π.

Now we multiply the 8 and 1/3 ==> 8/3*π cm² and put the π at the end. And that is the final simplified version. Sometimes the answer needs to be in decimal so we multiply 8/3 and π ==> 8.38 cm² and that is another possible result.

Example 2

Example 2

To find the area of the sector of a circle we need the radius and the central angle. Then we can use the formula, Area = πr²* θ/360°. Now our first step is substitute the radius and the central into the formula.

So we have Area of the Shaded Sector AB = π(6)² * (74°)/360°.

Next we square the number, 6, next to pi ==> 36π * (74°)/360°.

Now we simplify the 74 and the 360 by dividing each number by 2° ==> 36π * 37/180.

Next we simplify the two numbers 36 and 180 by dividing each number by 4 ==> 9*37/45*π.

Now we multiply the 9 and 37/45 ==> 333/45*π in² and put the π at the end. And that is the final simplified version. Sometimes the answer needs to be in decimal so we multiply 333/45 and π ==> 23.25 in² and that is another possible result.

Example 3

Example 3:

To find the area of the sector of a circle we need the radius and the central angle. Then we can use the formula, Area = πr²* θ/360°. Now our first step is substitute the radius and the central into the formula.

Our first step is to the area of the unshaded sector and to do that we subtract the total 360° and the shaded sector 120° ==> 240°.

Now we can use the formula, Area of the Shaded Sector ACB = π(5)² * (240°)/360°.

Next we square the number, 5, next to pi ==> 25π * (240°)/360°.

Now we simplify the 240 and the 360 by dividing each number by 120° ==> 25π * 2/3.

Next we can rearrange the numbers to put π at the end ==> 25*2/3*π.

Now we multiply the 25 and 2/3 ==> 50/3*π cm² and put the π at the end. And that is the final simplified version. Sometimes the answer needs to be in decimal so we multiply 50/3 and π ==> 52.36 cm² and that is another possible result.

Example 4

Example 4:

To find the area of the sector of a circle we need the radius and the central angle. Then we can use the formula, Area = πr²* θ/360°. Now our first step is substitute the radius and the central into the formula.

Our first step is to the area of the unshaded sector and to do that we subtract the total 360° and the shaded sector 260° ==> 100°.

Now we can use the formula, Area of the Shaded Sector ACB = π(10)² * (100°)/360°.

Next we square the number, 5, next to pi ==> π*100 * (100°)/360°.

Now we simplify the 100 and the 360 by dividing each number by 20° ==> π*100 * 5/18.

Next we simplify the 100 and the 18 by dividing each number by 2 ==> π*50 * 5/9.

Finally we multiply the 50 and 5/9 ==> 250/9*π m² and put the π at the end. And that is the final simplified version. Sometimes the answer needs to be in decimal so we multiply 250/9 and π ==> 87.27 m² and that is another possible result.

Live Worksheet 1

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Live Worksheet 2

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