The formula for finding the area of ​​a sector is A =

n °
/.
360 °

π × r2

Just use π = 3.14 and substitute the value of r and n in the formula to get the area. But what is a sector?

A sector is part of a circle bounded by two radii and their interrupted arc. Examples of sectors are shown below. The blue shaded part of the circle is the sector

The best example of a real life sector I can think of is a slice of pizza.

In the example above, a quarter of the pizza is removed and we can call it a sector. The next time you talk to a friend, you can tell them you ate part of a pizza. Was just a joke!

Therefore, to get the area of ​​this pizza slice, you need to find the area of ​​the circle and divide the result by 4

Visualizing things this way may help you see how they got the formula

For a 360 ° circle, A =

360 °
/.
360 °

π × r2

Notice that

360 °
/.
360 °

= 1 and 1 × π × r2 = π × r2.

Including 360 ° / 360 ° does not change the formula

For a 180 ° circle or half a circle, A =

180 °
/.
360 °

π × r2

For a 90 ° circle or a quarter of a circle, A =

90 °
/.
360 °

× π × r2

 In general, A = for a ° circle n ° /. 360 ° π × r2

## Be careful when calculating the area of ​​a sector: n must be positive and n must be less than 360 degrees

Example 1:

A circle has a radius of 5 cm. Calculate the area of ​​a sector if the angle of the radii is 60 °

A =

60 °
/.
360 °

× 3.14 × 52

A =

60 °
/.
360 °

× 3.14 × 25

A = 0.166 x 78.5 = 13.06 cm2

Example 2:

A pizza is 14 inches in diameter.

a. Calculate the area of ​​a slice of pizza when the chef has made all the slices at a 45 ° angle

b. How many slices do you think this pizza has?

c. What is the area of ​​the whole pizza without using the formula of the circular area?

A =

45 °
/.
360 °

× 3.14 × 142

A =

45 °
/.
360 °

× 3.14 × 196

A =

45 °
/.
360 °

X 615.44

A = 0.125 x 615.44 = 76.93 inches2

b. If all slices have been cut at the same angle, then all slices must be the same size.

Just ask yourself: “How many 45 ° are 360 ​​°?”

45 ° + 45 ° + 45 ° + 45 ° + 45 ° + 45 ° + 45 ° + 45 ° = 360 °

Or 8 × 45 ° = 360 °

The pizza has 8 slices

c. Since the pizza has 8 slices, the area of ​​the entire pizza is 8 inches by 76.93 inches2 = 615.44