Volume Formulas

Ever wondered how much stuff can fit inside different shapes? Volume formulas give us the answer! Let's explore the most common 3D shapes and how to find their volumes.

For simple shapes like a cube, just cube the side length: $a^3$ (multiply the side length by itself three times). A cuboid or rectangular prism uses length × width × height (l × b × h).

Circular-based shapes have special formulas. A cylinder (like a can) uses $\pi r^2h$ where r is the radius and h is height. A cone uses the same formula but multiplied by $\frac{1}{3}$, making it $\frac{1}{3}\pi r^2h$.

Spheres (perfect balls) have volume $\frac{4}{3}\pi r^3$, while a hemisphere (half a sphere) is $\frac{2}{3}\pi r^3$. For irregular shapes, prisms use base area × height, and pyramids use $\frac{1}{3}$ × base area × height.

Fun Fact: Understanding volume helps in real life! When you fill a water bottle, bake a cake, or help your family pack moving boxes, you're applying these volume concepts.