The diagrams show the cross-sections of two drawer handles. Shape X is a rectangle ABCD joined to
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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.
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Related Book For
Pearson Edexcel A Level Mathematics Pure Mathematics Year 2
ISBN: 9781292183404
1st Edition
Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran
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