Mensuration for a Cube of Total surface area 12996 square units: Volume, Surface Area, Diagonal and Circumradius

You are given a cube of Total surface area 12996 square units. 
So we may compute that the side equals √(surface-area)/2 = (area/4)0.5 = 57 units.

Computing the Total Surface Area, Volume and Diagonal of the cube

Side (or length) of the cube = 57 units. 
Total Surface area of the cube = 4 * side2 = 4 * 57 * 57 = 12996 square units.
Volume of the cube = side3 = 57 * 57 * 57 = 185193 cubic units. 
Length of the diagonal of the cube = (3 * side2)0.5 = 98.73 units  (Extending the Pythagorean theorem to three dimensions)


Circumsphere of the Cube


Mass of the cube = Density x Volume = 1659329.28 grams. 

All cubes are geometrically similar. 

The scale factor A : B = 57:19
Ratio of surface areas of A : B  = 12996: 1444 = 9 : 1 (this holds true whether you compare total surface area or surface area per side, or any corresponding pairs of surface areas between the cubes)
Ratio of volumes of A:B = 185193 : 6859 = 27 : 1



Some more example(s):

Geometric Properties of a cube of size 58 units: Properties like Surface Area, Volume, Circumradius, Circumsphere, Mensuration etc.

Geometric Properties of a cube of size 59 units: Properties like Surface Area, Volume, Circumradius, Circumsphere, Mensuration etc.
