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 circles to that between the two outer circles?

Step-by-step explanation:

The ratio of radii of the three concentric circles is 4 : 5 : 7

Let x be the common multiple. Then the radii of the three circles be 4x, 5x and 7x

Of these 4x and 5x radii circles lie in inner position and 5x and 7x radii circles lie in outer position.

Then the area between the inner circles is

= π (5x)² - π (4x)² unit²

= (25 - 16)πx² unit²

= 9πx² unit²

and the area between the outer circles is

= π (7x)² : π (5x)² unit²

= (49 - 25)πx² unit²

= 24πx² unit²

Therefore the ratio of the areas between the two inner circles to that between the two outer circles is

= 9πx² : 24πx²

= 3 : 8