Question 390223
<pre><font face = "batangche" size = 3 color = "indigo"><b>
A = {{{pi}}}rs

If the diameters are equal then the radii are too.

Suppose the curved area of the smaller cone is A<sub>1</sub> and the curved
area of the larger cone is A<sub>2</sub>. 

Suppose the slant height of the smaller cone is s<sub>1</sub> with radius r
and the slant height of the larger cone is s<sub>2</sub> with the same radius r.
 
Then we have

A<sub>1</sub> = {{{pi}}}rs<sub>1</sub>

and

A<sub>2</sub> = {{{pi}}}rs<sub>2</sub>

So we make the proportion:

{{{A[1]/A[2]}}}{{{""=""}}}{{{(pi*r*s[1])/(pi*r*s[2])}}}{{{""=""}}}{{{(pi*r*s[1])/(pi*r*s[2])}}}{{{""=""}}}{{{(cross(pi)*cross(r)*s[1])/(cross(pi)*cross(r)*s[2])}}}{{{""=""}}}{{{s[1]/s[2]}}}{{{""=""}}}{{{7/8}}}

So the areas of the curved surfaces are in the same ratio as their 
slant heights, or 7:8

Edwin</pre>