The diameter of two cones are equal if their slant height are in the ratio 5:4, find the ratio of their curved surface area

Answer 1

surface area of similar objects varies directly with the square of their corresponding sides

ratio of surface areas
= 5^2 : 4^2
= 25 : 16

Answer 2

Hmmm. I interpret the problem to be that the cones have the same diameter. Hence, the same base radius.

Since the curved surface area is πrs, if r is constant, then the area is proportional to s, so it is also in the ratio 5:4.