SOLUTION: the diameter of two cones are equal. if there slant hieght is in the ratio 7:8,then find the ratio of their curved suface area.

A = rs

If the diameters are equal then the radii are too.

Suppose the curved area of the smaller cone is A1 and the curved
area of the larger cone is A2. 

Suppose the slant height of the smaller cone is s1 with radius r
and the slant height of the larger cone is s2 with the same radius r.
 
Then we have

A1 = rs1

and

A2 = rs2

So we make the proportion:



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

Edwin