Curved surface area = π × r × l
Since the two cones have the same diameter, the radius should be the same (r).
As for the slanted height, since the ratio 7:4 is given, we can assume the slanted height is 7x and 4x. So, we can find the ratio of their curved surface area by eliminate the same factor (π r x) for the two terms (as shown below)
Ratio
= π r (7x) : π r (4x)
= 7:4
Therefore, the ratio between the curved surface area is also equal to 7:4.