PROBLEMS ON AREA OF SECTOR AND LENGTH OF ARC

Find the length of ZY. Round to the nearest hundredth.

Problem 1 :

Solution :

The formula to find the arc length is

= (Arc Measure / 360˚) ∙ 2πr

Substitute r = 4 in, arc measure = 75˚ and π = 3.14

= (75˚/360˚) × 2 × 3.14 × 4

= 5.23 in

So, the length of the arc is about 5 in. 

Problem 2 :

Solution :

The formula to find the arc length is

= (Arc Measure / 360˚) ∙ 2πr

Diameter = 10 cm

Substitute r = 5 cm, arc measure = 130˚ and π = 3.14

= (130˚/360˚) × 2 × 3.14 × 5

= 11.33 cm

So, the length of the arc is about 11 cm. 

Problem 3 :

Find the area of a sector if the circle has a radius of 10 centimeters and the central angle measures 72.

Solution :

Given, radius = 10 cm

Central angle = 72˚

A = (θ/360˚) ∙ πr²

= (72/360) × 3.14 × (10)²

= 1/5 × 3.14 × 100

A = 62.8 cm²

So, area of sector is 62.8 cm².

Problem 4 :

Find the area of a sector if the circle has a radius of 5 inches and the central angle measures 60.

Solution :

Given, radius = 5 inches

Central angle = 60˚

A = (θ/360˚) ∙ πr²

= (60/360) × 3.14 × (5)²

= 1/6 × 3.14 × 25

A = 13.08 in²

So, area of sector is 13.08 in².

Problem 5 :

If the area of a sector is 15π square centimeters and the radius of the circle is 5 centimeters, find the measure of the central angle.

Solution :

Given, area = 15π and radius = 5 centimeters

A = (θ/360˚) ∙ πr²

15π = (θ/360˚) ∙ π ∙ (5)²

θ = 15π × 360/π × 25

θ = 216˚

So, central angle of a sector is 216˚.