Question:
The radii of three concentric circles are in the ratio 2: 3: 4. What is the ratio of sum of areas of two inner circles to the area of the region between outermost circle and innermost circle?
The radii of three concentric circles are in the ratio 2: 3: 4. What is the ratio of sum of areas of two inner circles to the area of the region between outermost circle and innermost circle?
Updated On: Sep 10, 2024
- 12:11
- 13:12
- 15:11
- 10:7
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The Correct Option is B
Solution and Explanation
The correct option is (B): 13:12.
(Radius of circle)2 ∝ Area of circle
Let OA = 2x, OB = 3x and OC = 4x
Required ratio = (Sum of area of two inner circles): (Area of region between outermost circle and innermost circle)
= [(2x)2 + (3x)2 ]: [(4x)2 - (2x)2 ]
= (4 + 9): (16 - 4)
= 13:12.
(Radius of circle)2 ∝ Area of circle
Let OA = 2x, OB = 3x and OC = 4x
Required ratio = (Sum of area of two inner circles): (Area of region between outermost circle and innermost circle)
= [(2x)2 + (3x)2 ]: [(4x)2 - (2x)2 ]
= (4 + 9): (16 - 4)
= 13:12.
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