1) Arc Length, knowing Ф value, the central angle: 2π.R.(Ф/360°)
Length (Arc ACB) = 2π(8).(90/360) = 16π/4 = 4π
Perimeter ACBO = Length (Arc ACB) + OA + OB = 4π + 8 + 8
Perimeter ACBO = 4π+16 (answer)
2) Area of a circular sector = πR².(Ф/360°)
Area of right triangle AOB = AO.AB/2 = 8x8/2 = 64/2 = 32 (Needed later)
Area ACBO = π.8².(90°/360°) = 64.π.1/4 = 16π, BUT WE NEED the area limited between the arc and the chord:
Area bounded by cord and arc)=Area sector (ACB0) - Area right triangle AOB
Area bounded by cord and arc= 16π- 64/2.
Area bounded by cord and arc= 16π- 32 (answer D)