1. Solid Sphere:
  - Volume (V) is calculated as: 
  \[ V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (3 \, cm)^3 = 36\pi \, cm^3 \]
  - Total Surface Area (A) is calculated as: 
  \[ A = 4 \pi r^2 = 4 \pi (3 \, cm)^2 = 36\pi \, cm^2 \]

2. Solid Right Cone:
  - Volume (V) is calculated as: 
  \[ V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (3 \, cm)^2 * 12 \, cm = 36\pi \, cm^3 \]
  - Total Surface Area (A) is calculated as: 
  \[ A = \pi r (r + l) = \pi * 3 \, cm * (3 \, cm + sqrt((3 \, cm)^2 + (12 \, cm)^2)) = \pi * 3 \, cm * sqrt(153) \, cm \]

3. Solid Right Circular Cylinder:
  - Volume (V) is calculated as: 
  \[ V =  \pi r^2 h =  \pi (3 \, cm)^2 * 4\, cm = 36\pi\, cm^3\]
  - Total Surface Area (A) is calculated as: 
  \[ A = 2\pi rh + 2\pi r^2 = 2\pi*3cm*4cm + 2\pi*(3cm)^2 = 42\pi\, cm^2\]

From these calculations, we can see that:

- The volume of the sphere is equal to the volume of the cone and the cylinder, not greater.
- The volume of the cone is equal to the volume of the cylinder, not less.
- The total surface area of the cone is greater than that of the sphere only if \(sqrt(153) > 12\), which is true.
- The total surface area of the cylinder is greater than that of the sphere, not less.
- The total surface area of the cone is not equal to that of the cylinder.

So, the correct answer is: The total surface area of the cone is greater than that of the sphere.