Question

Describe the unit cube bounded by the planes x =0 and x=1.

Answer 1

The unit cube bounded by the planes x = 0 and x = 1 has a volume of 1 cubic unit.

Step-by-step explanation:

The unit cube is defined by the planes x = 0, x = 1, y = 0, y = 1, z = 0, and z = 1, forming a cube where all edges are of length 1 unit. Considering x = 0 and x = 1 as two parallel planes defining the cube's boundaries, the distance between these planes is 1 unit (1 - 0 = 1).

The formula for the volume of a cube is V =
`s^3`, where 's' is the length of one side. Here, each side of the cube is 1 unit long. So, V =
`1^3` = 1 cubic unit, indicating the volume of the cube.

Visually, the cube's edges along the x-axis span from x = 0 to x = 1, encapsulating a distance of 1 unit. Considering this, the cube occupies a unit volume, as its length, width, and height are all 1 unit. Hence, the volume of the cube bounded by x = 0 and x = 1 is 1 cubic unit.