passpadi

2002

Mathematics

JAMB

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 = 5/9πR2
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