2002
Mathematics
67ca00ce0c643c71d77dee1f
In the diagram above are two concentric circles of radii r and R respectively with center O. If r = 2/3R, express the area of the shaded portion in terms of π and R
A.
21/25πR2
B.
9/25πR2
C.
21/23πR2
D.
5/9πR2
Correct Answer: 5/9πR2
Explanation
r = 2/3R ∴R = 3/3R Area of small circle = πr2 = π(2R/3)2 Area of the big circle πr2 = π(3R/3)2 Area of shaded portion = π(3R/3)2 - π(2R/3)2 = π[(3R/3)2 - (2R/3)2] = π[(3R/3)+(2R/3) − (3R/3) - (2R/3)] = π[(5R/3) (R/3)] = π x 5R/3 x R3 = 5/9πR2
r = 2/3R ∴R = 3/3R Area of small circle = πr2 = π(2R/3)2 Area of the big circle πr2 = π(3R/3)2 Area of shaded portion = π(3R/3)2 - π(2R/3)2 = π[(3R/3)2 - (2R/3)2] = π[(3R/3)+(2R/3) − (3R/3) - (2R/3)] = π[(5R/3) (R/3)] = π x 5R/3 x R3 = 5/9πR2THIS WEEK's
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