Question

A sector of a circle has a diameter of 10 feet and an angle of 2π/3 radians. Find the area of the sector.

Answer 1

The area of the sector  2π/3 radians with diameter 10 feet 75π feet²

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

Diameter =  10 feet

radius = 5 feet

angle =   2π/3 radians

⇒angle= arc/radius

⇒  2π/3 radians° =arc/10

⇒ arc =2π/3 radians *10

 ⇒arc=2π/3 radians*10

⇒arc = 20/π43 feet

Area of a circle = π*r²

                        =  π*5² = π25

∵ area of complete circle is π25

∴ area of 2π/3 radians = π25/2π *2π/3 radians

                                     = 75π  answer

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