FIND RADIUS OF CIRCLE FROM THE GIVEN AREA OF SECTOR

What is area of sector ?

A section of a circle determined by a central angle and a corresponding circular arc.

To find area of sector, we use the formula 

A = (θ/360˚) ∙ πr²

Problem 1 :

A sector of a circle has central angle 45 and area 49π/8 cm². Find the radius of the circle.

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 45˚ and area = 49π/8 cm²

49π/8 = 45/360 ∙ πr²

49π/8 = 1/8 ∙ πr²

πr² = (49π/8) × 8

r² = 49

r = √49

r = 7 cm

So, the radius of the circle is 7 cm.

Problem 2 :

A sector of a circle has central angle 150 and area 5π/27 ft². Find the radius of the circle.

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 150˚ and area = 5π/27 ft²

5π/27 = 150/360 ∙ πr²

5π/27 = 5/12 ∙ πr²

πr² = 5π/27 × 12/5

r² = 4/9

r = √4/9

r = 2/3

r = 0.6 ft

So, the radius of the circle is 0.6 ft.

Problem 3 :

A sector of a circle has central angle 120˚ and area 16π/75 in². Find the radius of the circle.

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 120˚ and area = 16π/75 in²

16π/75 = 120/360 ∙ πr²

16π/75 = 1/3 ∙ πr²

πr² = 16π/75 × 3

r² = 16/25

r = √16/25

r = 4/5

r = 0.8 in

So, the radius of the circle is 0.8 in.

Problem 4 :

A sector of a circle has central angle 210˚ and area 21π/4 m². Find the radius of the circle.

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 210˚ and area = 21π/4 m²

21π/4 = 210/360 ∙ πr²

21π/4 = (7/12) ∙ πr²

πr² = (21π/4) × 12/7

r² = 9

r = √9

r = 3 m.

So, the radius of the circle is 3 m.

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