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

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The area of the cube of side s is given by s^3. Here we have the ends of one of the sides as (1,3,-1) and ( 4,-3,5)

The distance between the points

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

=> s = sqrt [ 3^2 + 6^2 + 6^2]

=> s = sqrt (9 + 36 + 36)

=> s = sqrt ( 72 + 9)

=> s = sqrt 81

=> s = 9

The volume of the cube is s^3 = 9^3 = 729 cubic units.

**The required volume is 729 cubic units.**

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.**