if the cones below are similar, what is the ratio of the slant height of the smaller cone to the larger cone when the Surface area of smaller cone is 52in and larger cone is 637in

Step-by-step explanation:

Given that,

The surface area of the big cone is 637 in²

A_b = 637 in²

The surface area of the small cone is 52 in²

A_s = 52in²

Then, surface area of a cone can be calculated using

A = πrL

Where r is radius and L is slant height

Then,

Since they are similar, the radius are equal

A_s = πrL_s

A_b = πrL_b

So, the ratio of the surface area of the small cone to the big cone area is

A_s / A_b = πrL_s / πrL_b

52 / 637 = L_s / L_b

4 / 49 = Ls / L_b

So, the ratio of slant small cone to slant height of big cone is 4:49