Can you show how this is true. In a 3D rectangular box, one face has area a, the other b, the third c. So...

...the volume is the sq root of a*b*c. How come?Can you show how this is true. In a 3D rectangular box, one face has area a, the other b, the third c. So...
let x,y and z = lengths of sides of the box


area a = xy


area b = yz


area c = xz





volume = xyz = sqrt [(x^2)(y^2)(z^2)]


=sqrt(xy*yz*xz)


from above, volume = sqrt(a*b*c)Can you show how this is true. In a 3D rectangular box, one face has area a, the other b, the third c. So...
Volume is equal to the length*width*height or in your case a*b*c. It is not the square root of that calculation.





Think of it this way. The (suface) area is length*width. By multiplying the height, you determine the amount of space occupied by the object. As you can see in the equations, area is a two dimensional calculation and volume is three dimensional.
One side has width, one side has height and one had depth. All combined equals volume.