To recall, a sector is a section of a one enclosed between its 2 radii and the arc adjoining them.

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For example, a pizza part is an example of a ar representing a portion of the pizza. There room two varieties of sectors, minor and significant sector. A minor sector is less than a semi-circle sector, whereas a significant sector is a sector the is higher than a semi-circle.

In this article, you will certainly learn:

What the area that a sector is.How to discover the area that a sector; andThe formula for the area that a sector.

 

What is the Area of a Sector?

The area of a ar is the an ar enclosed by the 2 radii of a circle and the arc. In an easy words, the area of a sector is a fraction of the area of the circle.

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Solution

Area of a sector = (θ/360) πr2

= (130/360) x 3.14 x 28 x 28

= 888.97 cm2

Example 2

Calculate the area of a sector with a radius that 10 yards and also an angle of 90 degrees.

Solution

Area the a ar = (θ/360) πr2

A = (90/360) x 3.14 x 10 x 10

= 78.5 sq. Yards.

Example 3

Find the radius of a semi-circle v an area that 24 inch squared.

Solution

A semi-circle is the same as half a circle; therefore, the angle θ = 180 degrees.

A= (θ/360) πr2

24 = (180/360) x 3.14 x r2

24 = 1.57r2

Divide both sides by 1.57.

15.287 = r2

Find the square root of both sides.

r = 3.91

So, the radius of the semi-circle is 3.91 inches.

Example 4

Find the main angle that a sector who radius is 56 cm and the area is 144 cm2.

Solution

A= (θ/360) πr2

144 = (θ/360) x 3.14 x 56 x 56.

144 = 27.353 θ

Divide both political parties by θ.

θ = 5.26

Thus, the main angle is 5.26 degrees.

Example 5

Find the area that a sector with a radius the 8 m and a main angle of 0.52 radians.

Solution

Here, the main angle is in radians, so we have,

Area the a sector = (θr2)/2

= (0.52 x 82)/2

= 16.64 m2

Example 6

The area of a ar is 625mm2. If the sector’s radius is 18 mm, find the main angle the the ar in radians.

Solution

Area of a sector = (θr2)/2

625 = 18 x 18 x θ/2

625 = 162 θ

Divide both political parties by 162.

θ = 3.86 radians.

Example 7

Find the radius of a sector who area is 47 meters squared and main angle is 0.63 radians.

Solution

Area that a ar = (θr2)/2

47 = 0.63r2/2

Multiply both sides by 2.

94 = 0.63 r2

Divide both political parties by 0.63.

r2 =149.2

r = 12.22

So, the radius the the ar is 12.22 meters.

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Example 8

The size of an arc is 64 cm. Discover the area of the sector created by the arc if the circle’s radius is 13 cm.