150 square centimetres is a measure of area. Assuming it is the total surface area of the cube, the surface area of any one [square] face is 150/6 = 25 sq cm. Consequently, the width and length are sqrt(25) = 5 cm.
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The volume of a square cuboid is length x height x width. A cube is a special type of cuboid in which all six faces are square. The three dimensions then become equal in length. So the volume of a cube is L3 where L is the length of any edge. The volume of a cube with an edge length of 4" is 43 = 64 in3 (or 64 cubic inches)
To calculate the area of one side of a cube, you need to find the area of one of the square faces. Since all sides of a cube are equal in length, you can use the formula for the area of a square, which is side length squared. Therefore, to find the area of one side of a cube, you simply square the length of one side of the cube.
The side of a square is is cube root of 2cm. Find the length of the diagonals.
Whatever it is, all three numbers are the same.
If it is a true cube, then the length = width = height. Therefore the length = cube root of 81 = 811/3 = 4.3267....inches.