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
If the diagonal is d thenV = [d/sqrt(3)]^3
You cannot. There is not enough information.
To get the largest cube of wood, you would want to cut it out so that the long diagonal is the diameter of the log: 25.4" For a cube of side length s, the diagonal is s√3, so to find the side given the diagonal, we need to divide by √3 25.4 / 1.732 = 14.664" This is one side of the cube, so the volume is 3153.69 cubic inches. ◄ As for total area, I am not sure what that is asking for. If it is surface area, 87.988 in² is the answer. ■
The answer depends on what information you are given: (volume, breadth and height), (surface are, breadth and height), (principle diagonal, breadth and height), (mass, density, breadth and height) or some other set.
Multiply them: density*volume = mass
The volume of an oblong is: volume = length x width x height As the box is cubical, ie is a cube, all sides are of equal length, thus: volume_cube = side x side x side = side3 So, given the volume: side = cube_root(volume) ie, take the cube root of the volume of 2.197cm3.
you don't. you have your teacher do that for you
If the diagonal is d thenV = [d/sqrt(3)]^3
The answer depends on what information is provided: the volume, total surface area, principal diagonal, minor diagonal, etc.
You cannot. There is not enough information.
The longest diagonal in a cube is equal to the length of the edge, multiplied by the square root of 3.
The length of each edge is: 1.5 meters.
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.
Volume = pi*r2*h
Volume = mass / density
To get the largest cube of wood, you would want to cut it out so that the long diagonal is the diameter of the log: 25.4" For a cube of side length s, the diagonal is s√3, so to find the side given the diagonal, we need to divide by √3 25.4 / 1.732 = 14.664" This is one side of the cube, so the volume is 3153.69 cubic inches. ◄ As for total area, I am not sure what that is asking for. If it is surface area, 87.988 in² is the answer. ■
The answer depends on what information you are given: (volume, breadth and height), (surface are, breadth and height), (principle diagonal, breadth and height), (mass, density, breadth and height) or some other set.