diagonal can only be found if two sides are known, imagine if you only have one known side ,the other side could be of any length and therefore the diagonal could be any length.
if two sides are known then use pythagoras, as the two sides make up the 'adjacent' and 'opposite' side of a right angled triangle
e.g. side a=2, side b=4 side c is square root of 2x2 plus 4x4
i.e root of 4+ 16=20 which is approx 4.47
Cool question ! Answer - half it then cube it to prove it - an example for you if cube diagonal (not square diagonal) is 100, then using pythagoras theorm the square diagonal = 70.71068, If square the square diagonal = 70.71068, then using pythagoras theorm the side length = 50 therefore the volume = 50 ^ 3 = 25000 units works with any numbers
You cube the edge length.
Find the cube root of the volume. Volume of a cube = length of side^3 therefore length of side = volume^(1/3)
The side length is the cube root of the volume.
If the diagonal is d thenV = [d/sqrt(3)]^3
The longest diagonal in a cube is equal to the length of the edge, multiplied by the square root of 3.
The side of a square is is cube root of 2cm. Find the length of the diagonals.
find the cube root of 125(which is 5) is the length of one side do Pythagorean theorem to find the diagonal 5squared plus 5 squared=50 square root of 50=7.07106781 is diagonal
Cool question ! Answer - half it then cube it to prove it - an example for you if cube diagonal (not square diagonal) is 100, then using pythagoras theorm the square diagonal = 70.71068, If square the square diagonal = 70.71068, then using pythagoras theorm the side length = 50 therefore the volume = 50 ^ 3 = 25000 units works with any numbers
You cube the edge length.
Given the length of the diagonal of the square ... call it 'D units'. The area of the square is (1/2 D2) (same units)2.
Find the cube root of the volume. Volume of a cube = length of side^3 therefore length of side = volume^(1/3)
The side length is the cube root of the volume.
If the diagonal is d thenV = [d/sqrt(3)]^3
Cube root the volume as for example if its volume was 27 then the cube root of 27 is 3 which is its side length
12 inches = 1 foot. 240 inches = 20 feet. Use Pythagoras' theorem to find the diagonal of one of the faces of the cube. 2402+2402 = 115200. The square root of 115200 is 339.411255 Therefore the diagonal of the cube is 339.411255 inches or 339 inches correct to three significant figures Incidentally, by using the above answer and Pythagoras' theorem we can also work out the length of the longest internal diagonal within the cube which works out exactly as 340 inches.
The last guy was wrong. Sorry