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.
Area of a sector = (θ/360) πr2
= (130/360) x 3.14 x 28 x 28
= 888.97 cm2
Calculate the area of a sector with a radius that 10 yards and also an angle of 90 degrees.
Area the a ar = (θ/360) πr2
A = (90/360) x 3.14 x 10 x 10
= 78.5 sq. Yards.
Find the radius of a semi-circle v an area that 24 inch squared.
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.
Find the main angle that a sector who radius is 56 cm and the area is 144 cm2.
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.
Find the area that a sector with a radius the 8 m and a main angle of 0.52 radians.
Here, the main angle is in radians, so we have,
Area the a sector = (θr2)/2
= (0.52 x 82)/2
= 16.64 m2
The area of a ar is 625mm2. If the sector’s radius is 18 mm, find the main angle the the ar in radians.
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.
Find the radius of a sector who area is 47 meters squared and main angle is 0.63 radians.
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.
r = 12.22
So, the radius the the ar is 12.22 meters.
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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.