Mathematics

In the diagram above, PQ and XY are two concentric arc; center O, the ratio…

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: Option C
Explanation

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

Length of arc PQ = (frac{theta}{360} times 2pi r = 1)

Length of arc XY = (frac{theta}{360} times 2pi R = 3)

Ratio of the arc = (frac{r}{R} = frac{360 times 2pi theta}{2pi theta times 360 times 3})

= (frac{1}{3})

Ratio of their area = ((frac{1}{3})^2 = frac{1}{9})

= 1 : 9