A cone is cut by a plane parallel to its base, half way up its height…

Step 1. The scale. The small cone has half the height, so every length is $\frac{1}{2}$ of the whole cone's.

Step 2. The volumes. The small cone has $\left(\dfrac{1}{2}\right)^3 = \dfrac{1}{8}$ of the whole cone. The frustum has $\dfrac{7}{8}$. The ratio is $\dfrac{7/8}{1/8} = 7$.

Step 3. The curved surfaces. The small cone has $\left(\dfrac{1}{2}\right)^2 = \dfrac{1}{4}$ of the curved surface of the whole cone. The frustum has $\dfrac{3}{4}$. The ratio is $3$.