PRACTICE QUESTIONS OF FINDING AREA OF SECTOR

Problem 1 :

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively.

Problem 2 :

Find the area of the sector whose radius and central angle are 21 cm and 60° respectively.

Problem 3 :

Find the area of the sector whose radius and central angle are 4.9 cm and 30° respectively.

Problem 4 :

Find the area of the sector whose radius and length of arc are 6 cm and 20 cm respectively.

Problem 5 :

Find the area of the sector whose diameter and length of arc are 10 cm and 40 cm respectively.

Problem 6 :

Find the area of the sector and also find the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm.

Problem 7 :

Find the area of the sector whose radius is 35 cm and perimeter is 147 cm.

Problem 8 :

Find the area of the sector whose radius is 20 cm and perimeter is 110 cm.

Detailed Answer Key

Problem 1 :

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively.

Solution :

Area of the sector  =  (θ/360°) ⋅ πr²

Substitute r = 42, θ = 60° and π ≈ 22/7

≈  (60°/360°)(22/7)(42)²

=  (1/6) ⋅ (22/7) ⋅ 42 ⋅ 42

=  924

So, the required area is about 924 cm²

Problem 2 :

Find the area of the sector whose radius and central angle are 21 cm and 60° respectively.

Solution:

Area of the sector  =  (θ/360°) ⋅ πr²

Substitute r = 21, θ = 60° and π ≈ 22/7

≈  (60°/360°)(22/7)(21)²

=  (1/6) ⋅ (22/7) ⋅ 21 ⋅ 21

=  231

So, the required ares is about 231 cm².

Problem 3 :

Find the area of the sector whose radius and central angle are 4.9 cm and 30° respectively.

Solution :

Area of the sector  =  (θ/360°) ⋅ πr²

Substitute r = 4.9, θ = 30° and π ≈ 22/7

≈  (30°/360°)(22/7)(4.9)²

=  (1/12) ⋅ (22/7) ⋅ 4.9 ⋅ 4.9

≈  6.3

So, the required area is about 6.3 cm².

Question 4 :

Find the area of the sector whose radius and length of arc are 6 cm and 20 cm respectively.

Solution :

Area of the sector  =  (lr/2) square units    

Substitute r = 6 and l = 20 

=  (20 ⋅ 6) / 2

=  60 cm²

Question 5 :

Find the area of the sector whose diameter and length of arc are 10 cm and 40 cm respectively.

Solution :

Diameter  =  10 cm

Radius  =  Diameter / 2  =  10/2  =  5 cm  

Area of the sector is

=  (lr/2) square units

Substitute r  =  5 and l  =  40 

=  (40 ⋅ 5) / 2

=  100 cm²

Problem 6 :

Find the area of the sector and also find the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm.

Solution :

Area of the sector  =  lr/2 

Substitute r = 21 and l = 66. 

=  (66 x 21) / 2

=  693 cm²

Using the area of the sector 693 cm², find the central angle θ.  

Area of the sector  =  693 cm²

(θ/360°) ⋅ πr²  =  693

Substitute r = 21 and π ≈ 22/7.

(θ/360) ⋅ (22/7) ⋅ 21²  =  693

 (θ/60°) ⋅  231  =  693

θ  =  693 ⋅  (60°/231)

θ  =  180°

Problem 7 :

Find the area of the sector whose radius is 35 cm and perimeter is 147 cm.

Solution :

Given : Radius is 35 cm and perimeter of the sector is 147 cm. 

Perimeter of sector  =  147 cm

l + 2r  =  147 

l + 2(35)  =  147

l + 70  =  147

 l  =  77 cm

Area of the sector is

=  (lr/2) square units

Substitute r = 35 and l = 77

=  (77 ⋅ 35) / 2

=  2695/2

=  1347.5 cm²

Problem 8 :

Find the area of the sector whose radius is 20 cm and perimeter is 110 cm.

Solution :

Given : Radius is 20 cm and perimeter of the sector is 110 cm. 

Perimeter of sector = 110 cm

l + 2r  =  110

l + 2(20)  =  110

l + 40  =  110

l  =  70 cm

Area of the sector is

=  (lr/2) square units

Substitute r = 20 and l = 70. 

=  (70 x 20) / 2

=  700 cm²

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