Question

The central angle of an arc measures 75°. The diameter of the circle measures 6 meters. What is the area of the sector to the nearest tenth of a square meter? PLEASE HELP

Answer 1

The area of the sector is 5.9 m²

Step-by-step explanation:

The problem pertains to the area of an arc.

We know that area of the arc is given by= (central angle/360°)*π*r ²

Where r is the radius of the circle= diameter/2

Here diameter of the circle= 6 m

⇒Radius= 6/2= 3m

Substituting the values of the central angle as 75° (given), “r” as 3m, we get-

⇒Area of the sector= (75°/360°)*3.14*(3) ²

⇒Area of the sector=0.20834*3.14*9

⇒Area of the sector=5.9 m² (rounded off to the nearest tenth place after decimal)

Hence, area of the sector is 5.9 m²