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In the diagram above, PQ and XY are two concentric arc; c...

In the diagram above, PQ and XY are two concentric arc; center O, the ratio of the length of the two arc is 1:3, find the ratio of the areas of the two sectors OPQ and OXY

In the diagram above, PQ and XY are two concentric arc; center O, the ratio of the length of the two arc is 1:3, find the ratio of the areas of the two sectors OPQ and OXY

A.

1:3

B.

1:6

C.

1:9

D.

2:3

E.

4:9

Correct answer is C

Let the radius of the arc PQ = r and the radius of the arc XY = R.

Length of arc PQ = θ360×2πr=1

Length of arc XY = θ360×2πR=3

Ratio of the arc = rR=360×2πθ2πθ×360×3

= 13

Ratio of their area = (13)2=19

= 1 : 9