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˚.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM