Find the volume of the cube if endpoints of one of the sides are ( 1,3,-1) and ( 4,-3,5)

Given the endpoints of one of the sides of a cube are (
1,3,-1) and (4,-3,5)

Let us calculate the length of the
side using the distance formula.

==> D = sqrt(
x1-x2)^2 + 9y1-y2)^2 + (z1-z2)^2]

==> D = sqrt[ (
1-4)^2 + (3+3)^2 + (-1-5)^2]

==> D = sqrt( 3^2 + 6^2
+ -6^2 )

==> D = sqrt( 9+ 36+36) = sqrt81 =
9

Then the length of the side of the cube is 9
units.

Now we will calculate the
volume.

We know that the volume is given by
:

V = side^3 = 9^3 =
729

Then the volume of the cube is
V = 729 cubic units.