Question

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 1

The correct answer is 25:16

Explanation:

Answer 2

25:16 is the surface area of the cones.

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=
`(5)/(4)`

Now, let x be the surface area of the larger cone

and let y be the surface are of smaller cone.

∴
`z^(2) = (x)/(y)`

next substituting the value of z ,

⇒
`((5)/(4) )^(2) =(x)/(y)`

∴
`(x)/(y) = (25)/(16)`

The ratio for the surface area of cones is 25:16