Question

Four concentric circles are given. the radius of 1st circle is x.next is 2x,then 3x and 4x. given that area b/w 2nd and 1st is a and 4th and 3rd circles being

b.find ratio of a to b

Answer 1

$a = \pi( {(2x)}^{2} - {x}^{2} ) = 3\pi {x}^{2} \\ b = \pi( {(4x)}^{2} - {(3x)}^{2} ) = 7\pi {x}^{2} \\ therefore \\ \frac{a}{b} = \frac{3}{7}$
Ratio is 3:7