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
1:3
1:6
1:9
2:3
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
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