# AREA OF SECTOR OF CIRCLE

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

Calculate the sector area:

Problem 1:

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 90˚, radius = 16 in and π = 3.14

A = 90/360 ∙ (3.14) (16)²

A = 1/4 × 803.84

A = 200.96 in²

So, the area of the sector is about 200.96 in².

Problem 2 :

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 135˚, radius = 8 m and π = 3.14

A = 135/360 ∙ (3.14) (8)²

A = 3/8 × 200.96

A = 75.36 m²

So, the area of the sector is about 75.36 m².

Problem 3 :

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 40˚, radius = 18 m and π = 3.14

A = 40/360 ∙ (3.14) (18)²

A = 1/9 × 3.14 × 18 × 18

A = 113.04 m²

So, the area of the sector is about 113.04 m².

Problem 4 :

The area of a circle is 225π square inches. Find the area of the sector whose central angle is 45˚.

Solution :

Given, area of circle = 225π square inches

Central angle θ = 45˚

A = (θ/360˚) ∙ πr²

= (45˚/360˚) × 225π

= 1/8 × 225π

A = 28.125π square inches

So, area of the sector is 28.125π square inches.

Problem 5 :

The central angle of a sector is 60˚ and the area of the circle is 144π. What is the area of the sector?

Solution :

Given, area of circle = 144π

Central angle θ = 60˚

A = (θ/360˚) ∙ πr²

= (60˚/360˚) × 144π

= 1/6 × 225π

A = 24π

So, area of the sector is 24π.

Problem 6 :

A circle has a radius of 12. Find the area of the sector whose central angle is 120˚.

Solution :

Given, radius of circle = 12

Central angle θ = 120˚

A = (θ/360˚) ∙ πr²

= (120˚/360˚) × π × (12)²

= 1/3 × 144π

A = 48π

So, area of the sector is 48π.

Problem 7 :

Find the radius of a circle which has a sector area of 9π whose central angle is 90˚.

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 90˚ and area = 9π

9π = 90/360 ∙ πr²

9π = 1/4 ∙ πr²

πr² = 9π × 4

r² = 36

r = √36

r = 6

So, the radius of the circle is 6.

Problem 8 :

The central angle of a sector is 72˚ and the sector has an area of 5π. Find the radius.

Solution :

The formula to find area of the sector is

A = (θ/360˚) ∙ πr²

Substitute θ = 72˚ and area = 5π

5π = 72/360 ∙ πr²

5π = 1/5 ∙ πr²

πr² = 5π × 5

r² = 25

r = √25

r = 5

So, the radius of the circle is 5.

Problem 9 :

Find the measure of the central angle of a sector if its area is 5π and the radius is 6.

Solution :

Given, area = 5π and radius = 6

A = (θ/360˚) ∙ πr²

5π = (θ/360˚) ∙ π ∙ (6)²

θ = 5π × 360/π × 36

θ = 50˚

So, central angle of a sector is 50˚.

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