🧮 Understanding Volume Formulas
The volume formula is used to calculate the amount of space a 3D shape occupies. Each geometric solid — such as a cube, cylinder, cone, or sphere — has a unique formula based on its dimensions. Learning how to apply these geometry volume formulas helps students and professionals measure capacity, design objects, and solve real-world math problems.
Our table below lists the most common volume formulas for key geometric shapes, complete with diagrams, clear equations, and short explanations. From simple cubes to complex cones, each formula shows the relationship between height, radius, and base area. Whether you’re studying geometry or working on engineering and design tasks, this guide makes understanding volume formulas quick and practical.
| Shape | Image | Formula | Short description |
|---|---|---|---|
| Cube | V = a³ | Volume equals the cube of the side length. | |
| Parallelepiped | V = a × b × c × sin(θ) | Product of edge lengths and sine of included angle. | |
| Regular Prism | V = B × h | Base area multiplied by prism height. | |
| Cylinder | V = πr²h | Circle area of base times height. | |
| Cone | V = (1/3)πr²h | One-third of a cylinder with same base and height. | |
| Sphere | V = (4/3)πr³ | Volume proportional to the cube of the radius. |