Question

the diameters of two silver disc are in the ratio 2:3
what will be the ratio of their areas

Answer 1

there are two discs D1 and D2
As the ratio of diameters as 2:3
 so,let diameter of D1 as 2x
and radius of D1 as x
and similarly of D2 as 3x
and radius of D3 as 3x/2
then A.T.Q.
pi x x2= pi x (3x/2)^2
x2=9x2/4
so the ratio = 9:4

Answer 2

 The scale factor is k= 2/3 so all linear measurements (radii, diameters, circumferences) will have a ratio of 2/3. 

Then the ratio of the areas is k^2= (2/3)^2= 4/9 

Hoping this helps!