Volume of a Rectangular Prism

Find the volume of a cube, where the dimensions of the cube are defined by: $0 \leq x \leq 3$, $0 \leq y \leq 4$, $0 \leq z \leq 2$.

When tackling the calculation of the volume of a cube or rectangular prism, it's essential to grasp the fundamental concept that volume is a measure of the amount of space enclosed within a 3D object. The basic formula to determine the volume of a rectangular prism is to multiply its length, width, and height. In this problem, you are given the dimensions along the x, y, and z axes, which help in visualizing and computing the enclosed spatial volume.

When dealing with 3D geometry problems such as this, it's also beneficial to think about the properties that define various solid shapes. Understanding that a cube is a special type of rectangular prism where all sides are equal can simplify the volume calculation when this is the case. But more broadly, knowing how to handle 3D shapes with non-uniform dimensions is a key skill, especially in a calculus or geometry context where you often interpret or manipulate such shapes geometrically or even algebraically.

For this problem, recognizing the provided ranges for x, y, and z gives bounds on the dimensions of the rectangular prism. It's critical to interpret these bounds correctly to set up your volume calculation appropriately, essentially visualizing them as constraints that define the size and shape of the prism in 3-dimensional space.