To recall, a sector is a portion of a circle enclosed between its two radii and the arc adjoining them. For example, a pizza slice is an example of a sector representing a fraction of the pizza. There are two types of sectors, minor and major sector. A minor sector is less than a semi-circle sector, whereas a major sector is a sector that is greater than a semi-circle. In this article, you will learn:
What is the Area of a Sector?The area of a sector is the region enclosed by the two radii of a circle and the arc. In simple words, the area of a sector is a fraction of the area of the circle.  How to Find the Area of a Sector?To calculate the area of a sector, you need to know the following two parameters:
With the above two parameters, finding the area of a circle is as easy as ABCD. It is just a matter of plugging in the values in the area of the sector formula given below. Formula for area of a sectorThere are three formulas for calculating the area of a sector. Each of these formulas is applied depending on the type of information given about the sector. Area of a sector when the central angle is given in degreesIf the angle of the sector is given in degrees, then the formula for the area of a sector is given by, Area of a sector = (θ/360) πr2 A = (θ/360) πr2 Where θ = the central angle in degrees Pi (π) = 3.14 and r = the radius of a sector. Area of a sector given the central angle in radiansIf the central angle is given in radians, then the formula for calculating the area of a sector is; Area of a sector = (θr2)/2 Where θ = the measure of the central angle given in radians. Area of a sector given the arc lengthGiven the length of the arc, the area of a sector is given by, Area of a sector = rL/2 Where r = radius of the circle. L = arc length. Let’s work out a couple of example problems involving the area of a sector. Example 1 Calculate the area of the sector shown below. 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 of 10 yards and an angle of 90 degrees. Solution Area of a sector = (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 with an area of 24 inches 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 central angle of a sector whose 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 sides by θ. θ = 5.26 Thus, the central angle is 5.26 degrees. Example 5 Find the area of a sector with a radius of 8 m and a central angle of 0.52 radians. Solution Here, the central angle is in radians, so we have, Area of a sector = (θr2)/2 = (0.52 x 82)/2 = 16.64 m2 Example 6 The area of a sector is 625mm2. If the sector’s radius is 18 mm, find the central angle of the sector in radians. Solution Area of a sector = (θr2)/2 625 = 18 x 18 x θ/2 625 = 162 θ Divide both sides by 162. θ = 3.86 radians. Example 7 Find the radius of a sector whose area is 47 meters squared and central angle is 0.63 radians. Solution Area of a sector = (θr2)/2 47 = 0.63r2/2 Multiply both sides by 2. 94 = 0.63 r2 Divide both sides by 0.63. r2 =149.2 r = 12.22 So, the radius of the sector is 12.22 meters. Example 8 The length of an arc is 64 cm. Find the area of the sector formed by the arc if the circle’s radius is 13 cm. Solution Area of a sector = rL/2 = 64 x 13/2 = 416 cm2. Example 9 Find the area of a sector whose arc is 8 inches and radius is 5 inches. Solution Area of a sector = rL/2 = 5 x 8/2 = 40/2 = 20 inches squared. Example 10 Find the angle of a sector whose arc length is 22 cm and the area is 44 cm2. Solution Area of a sector = rL/2 44 = 22r/2 88 = 22r r = 4 Hence, the radius of the sector is 4 cm. Now calculate the central angle of the sector. Area of a sector = (θr2)/2 44 = (θ x 4 x 4)/2 44 = 8 θ θ =5.5 radians. Therefore, the central angle of the sector is 5.5 radians. 2.Twelve days befire Valentine's Day, Carl decided to give Nicole flowers. On the first day, he sent 1 red rose, on the second day, 3 red roses, on th … factor the trinomial using ac method,andcomplete the table,write the missing term on the blank table 5x²+11x+2 Patulong namn sa mathematicsWag nang sumagot pag d alam Yung answer factor completelyx⁴ -16 perform the indicated operation 1.) 7 + 15 =2.) -9 + 14 =3.) -6 + ( -17 ) =4.) -3 + 1 = 8 25.) -5 + -2 = 6 36. (8)(15) =7. (-4)(7) = … find the missing term of arithmetic sequence in 55, __ , __ , __ , __ ,90 find the next term of harmonic sequence 2/3,1/2,2/5. fine the discriminant then write the nature of the Roots 3ײ-22×+7= G11 ABM ENG SET A 17 Instructions: 5 Nikolai BUSINESS MATHEMATICS 1 Nikolai, Ella and Shaina are partners with a profit and loss sharing ratio of 3:3 … C 18 best answer. Take note of the item that you were not able to answer correctly and find the right swer as you go through this module. 13 Kongathio …
Solution: We use the formula for the area of the sector of a circle. The formula for the area of the sector of a circle with radius 'r' and angle θ = (θ/360°) × πr2 Given, θ = 60°, Radius = 6 cm Area of the sector = (θ/360°) × πr2 = 60°/360° × 22/7 × 6 × 6 = 132/7 cm2 ☛ Check: NCERT Solutions Class 10 Maths Chapter 12 Video Solution: NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.2 Question 1 Summary: The area of a sector of a circle with radius 6 cm is 132/7 cm2 if angle of the sector is 60°. ☛ Related Questions: Math worksheets and |
Given the area of the sector of radius 6cm and its central angle is 70 what is the area of sector
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