Calculating Area Of A Circle With A Sector Removed

What is the area of a circle with a diameter of 2 ft after a sector of 60° has been removed?

Given:

           Diameter = 2 ft

Sector removed = 60°

What is asked:

Area of a circle after 60° has been removed

Solution:

1. Solving for radius.

              Radius = Diameter ÷ 2
                          = 2 ft ÷ 2
                          = 1 ft

2. Now this is the formula in getting the area of a circle.

Area of a circle = π r² × (360° - 60°)

                                            360°

                        = 3.1416 × (1 ft)²  × (360° - 60°)
                                                              360°
                        = 3.1416 × 1 ft² × (300°)
                                                      360°
                        = 3.1416 ft² × 0.83333
                        = 2.62 ft² is the area of a circle with 60 sector removed
                     

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