FINDING AREA OF SECTOR OF A CIRCLE

Problem 1 :

Find the area of the sector having the central angle as follows.

Solution :

Area of sector = (θ/360) × πr²

θ = 70º, r = 10

= (70/360) × π (10)²

= 19.44 π square units.

Problem 2 :

Calculate the sector area.

Solution :

θ is the angle of the sector.

r is the radius of the circle.

Converting radian as degree measure, we get

Degree = (180/π) × (2π/9)

 = 40

To find area of the sector :

Method 1 :  

Method 2 :

Area of the sector is 

The required area is 113.08 m²

Problem 3 :

Given a central angle of 125º, find the area of sector in a circle of radius 7 cm. Round to the nearest tenth.

Solution :

Given a central angle θ = 125º.

Radius of a circle r = 7 cm

Area of sector :

So, nearest tenth is 53.42 cm²

Problem 4 :

Find the area of a sector if the central angle measures 30º radians and the radius of the circle is 11 cm.

Solution :

Central angle measures 30º radians.

Radius of the circle is 11 cm.

To find area of a sector :

Area of sector is 31.53 cm²

Problem 5 :

Find the area of the shaded region.

Solution :

Radius r = 10

Area of shaded region

= Area of a quadrant - Area of a triangle

= (1/4) πr² - 1/2 × b × h

= (1/4) x 3.14 × 10 × 10 - 1/2 × 10 × 10

= 78.5 - 50

= 28.5 cm²

So, area of shaded region is 28.5 cm²

Problem 6 : 

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

Solution :

Given central angle of a sector is 60º.

area of the circle is 144π.

πr² = 144π

r² = 144

r = 12

To find the area of the sector :

Area of sector = 75.51 square units.