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

Examples of sectors

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

A slice of pizza is a sector

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

Angular sector

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





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