The diagram shows a metal plate made by fixing together two pieces, OABCD (shaded) and OAED (unshaded). The piece OABCD is a minor sector of a circle with centre O and radius 2r. The piece OAED is a major sector of a circle with centre O and radius r. Angle AOD is α radians. Simplifying your answers where possible, find, in terms of α, π and r,

i. The perimeter of the metal plate,

ii. The area of the metal plate.
It s now given that the shaded and unshaded pieces are equal in area.

iii. Find α in terms of π.

Transcribed Image Text:

E 0Jarad D B