Mensuration for a Cube of diagonal 105.655 units: Volume, Surface Area, Diagonal and Circumradius

You are given a cube of diagonal 105.655 units. 
So we may compute that the side = diagonal/√3 = 61 units.

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

Side (or length) of the cube = 61 units. 
Total Surface area of the cube = 4 * side2 = 4 * 61 * 61 = 14884 square units.
Volume of the cube = side3 = 61 * 61 * 61 = 226981 cubic units. 
Length of the diagonal of the cube = (3 * side2)0.5 = 105.66 units  (Extending the Pythagorean theorem to three dimensions)


Circumsphere of the Cube


Mass of the cube = Density x Volume = 58561.1 pounds. 

All cubes are geometrically similar. 

The scale factor A : B = 61:1
Ratio of surface areas of A : B  = 14884: 1 = 3721 : 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 = 226981 : 1 = 226981 : 1



Some more example(s):

Geometric Properties of a cube of size 62 units: Properties like Surface Area, Volume, Circumradius, Circumsphere, Mensuration etc.

Geometric Properties of a cube of size 63 units: Properties like Surface Area, Volume, Circumradius, Circumsphere, Mensuration etc.
