The radii of three concentric circles are in the ratio of 4 : 5 : 7. What is the ratio of the area between the two inner circlesto that between the two outer circles?
Show answer & explanation
Correct answer: C
Explanation
Correct answer is option 3 i.e. 3 : 8
|
Concept |
Understanding |
Application |
Fair calculation |
|
Area of circle = πr2 |
The ratio of radii of the three concentric circles is 4 : 5 : 7 |
Then the area between the inner circles is = π (5x)2- π (4x)2 unit2 = 9πx2 unit2 |
52 – 42 = 25 – 16 = 9 |
|
Let the radii of the three circles be 4x, 5x and 7x |
Area between the outer circles is = π (7x)2 - π (5x)2 unit2 = 24πx2unit2 |
72 – 52 = 49 – 25 = 24 |
|
|
|
|
Required ratio = 9πx2 : 24πx2 = 3 : 8 |
|