what is the ratio for the surface areas of the cones shown below, given that they are similar and that the ratio of their radii and altitudes is 5:4?

Answer:25:16 is the surface area of the cones.Step-by-step explanation:Given: The ratio of their radii and altitudes is 5:4.Area of similar figures are proportional to the squares of their corresponding sides and this ratio is called scale factor.Let z be the scale factor∴z= [tex]\frac{5}{4}[/tex]Now, let x be the surface area of the larger cone      and let y be the surface are of smaller cone.∴ [tex]z^{2} = \frac{x}{y}[/tex]next substituting the value of z ,⇒[tex](\frac{5}{4} )^{2} =\frac{x}{y}[/tex]∴ [tex]\frac{x}{y} = \frac{25}{16}[/tex]The ratio for the surface area of cones is 25:16