The diagrams show the cross-sections of two drawer handles. Shape X is a rectangle ABCD joined to a semicircle with BC as diameter. The length AB = d cm and BC = 2d cm. Shape Y is a sector OPQ of a circle with centre O and radius 2d cm. Angle POQ is θ radians. Given that the areas of shapes X and Y are equal,

a. Prove that θ = 1 + π/4

Using this value of θ, and given that d = 3, find in terms of π:

b. The perimeter of shape X.

c. The perimeter of shape Y.

d. Hence find the difference, in mm, between the perimeters of shapes X and Y.

Transcribed Image Text:

2d A D d B C Shape X 2d Shape Y P Q