### Mensuration for a Cube of diagonal 102.191 units: Volume, Surface Area, Diagonal and Circumradius

You are given a cube of diagonal 102.191 units.
So we may compute that the side = diagonal/√3 = 59 units.

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

Side (or length) of the cube = 59 units.
Total Surface area of the cube = 4 * side2
Volume of the cube = side3
Length of the diagonal of the cube = (3 * side20.5

You might also make these calculations by considering the cube to be a special case of other 3D hexahedrons: an equilateral cuboid or a regular square prism or a square parallelopiped.

### Circumsphere of the Cube

A sphere touching all six vertices of a cube is known as its circumsphere.
The circumsphere of this cube as a radius equal to (length of the diagonal)/2 = 51.1

Now, if we know that the cube is made of Aluminum and we measure the side in inches and the density of the material is 0.258 pounds per cubic inch, we can calculate the mass of the cube:
Mass of the cube = Density x Volume = 52987.78 pounds.

All cubes are geometrically similar.

Let's compare this current cube (let's call it cube A) with a cube B of side 1 units
The scale factor A : B = 59:1
Ratio of surface areas of A : B  = 13924: 1 = 3481 : 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 = 205379 : 1 = 205379 : 1

You may find some more useful notes and information about the cube over here

Some more example(s):

Geometric Properties of a cube of size 60 units: Properties like Surface Area, Volume, Circumradius, Circumsphere, Mensuration etc.

Geometric Properties of a cube of size 61 units: Properties like Surface Area, Volume, Circumradius, Circumsphere, Mensuration etc.

properties of a Cube tutorial over hereCommon CoreGCSE