Understanding the volume of three-dimensional shapes is a fundamental skill in geometry that applies to everything from packaging design to architecture. In this guide, we will break down the formulas for Cubes, Prisms, and Cylinders in a way that is easy to understand and apply.
Volume is defined as the total amount of space occupied by a three-dimensional object. It is measured in cubic units, such as cubic centimeters (cm³), cubic meters (m³), or cubic inches (in³).
1. Volume of a Cube
A cube is the simplest 3D shape, where all sides (length, width, and height) are equal. Because every edge has the same length, we often refer to the side length as s or a.
The Formula:
Volume = s³ (or Side × Side × Side)
| Variable | Description |
| s | The length of one side (edge) of the cube |
Example: If a cube has a side length of 5 cm, its volume would be:Volume = 5 × 5 × 5 = 125 cm³
2. Volume of a Rectangular Prism
A rectangular prism (also known as a cuboid) is a solid object which has six faces that are rectangles. To find its volume, you simply multiply its three dimensions.
The Formula:
Volume = l × w × h
| Variable | Description |
| l | Length of the base |
| w | Width of the base |
| h | Vertical height of the prism |
Example: A box with a length of 10 cm, a width of 4 cm, and a height of 6 cm has a volume of:Volume = 10 × 4 × 6 = 240 cm³
3. Volume of a Cylinder
A cylinder is a 3D shape with two parallel circular bases connected by a curved surface. To calculate its volume, we first find the area of the circular base and then multiply it by the height.
The Formula:
Volume = π × r² × h
| Variable | Description |
| π (Pi) | Approximately 3.14159 |
| r | Radius of the circular base |
| h | Height of the cylinder |
Example: A soda can with a radius of 3 cm and a height of 12 cm has a volume of:Volume = 3.14 × (3)² × 12 ≈ 339.12 cm³
Summary Table of Formulas
| Shape | Formula | Key Variables |
| Cube | V = s³ | s = side |
| Rectangular Prism | V = l × w × h | l = length, w = width, h = height |
| Cylinder | V = πr²h | r = radius, h = height |
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