To find the ratio of curved surface area to the volume of a sphere, we first need to calculate the curved surface area and volume of the sphere.

**Curved Surface Area of a Sphere:**
The curved surface area of a sphere is given by the formula: CSA = 4πr², where r is the radius of the sphere.

**Volume of a Sphere:**
The volume of a sphere is given by the formula: V = 4/3πr³.

Since we are given the diameter of the sphere, we need to find the radius first.

**Finding the Radius:**
The diameter is given as 14 cm, which means the radius is half of that, i.e., 7 cm.

**Calculating the Curved Surface Area:**
Substituting the value of the radius into the formula for curved surface area, we get CSA = 4π(7)² = 4π(49) = 196π cm².

**Calculating the Volume:**
Substituting the value of the radius into the formula for volume, we get V = 4/3π(7)³ = 4/3π(343) = 4/3π(343) = 4/3 * 2401π = 3204π cm³.

**Calculating the Ratio:**
To find the ratio of curved surface area to volume, we divide the curved surface area by the volume:
Ratio = CSA / V = (196π) / (3204π) = 196 / 3204.

Simplifying the ratio, we get 1 / 16.

Therefore, the ratio of the curved surface area to the volume of the sphere is 1:16.

Since none of the given options match the correct ratio, it appears that there may be an error in the answer choices provided.