Interesting geometric relationships

Check out these relationships:

• The derivative of the formula for the volume of a sphere is the formula for the surface area of a sphere.
• The derivative of the formula for the volume of a cone is the formula for the base of a cone.
• The derivative of the formula for the area of a circle is the formula for the diameter of a circle.
• The first derivative of the formula for the volume of a sphere is 4*(area of a circle). The second derivative of the formula for the volume of a sphere is 4*(diameter of a circle).
• The derivative of the formula for the volume of a cylinder is (diameter of the base)*(height) + (area of the base).

So interesting! Could it have implications for dimensions beyond the three we know of?