Volume of 3D Shapes

**Volume** is the amount of space inside a 3D shape. How much water can a fish tank hold? How much dirt fills a box? How much cereal is in the cereal box? Those are all volume questions. And for boxes and other "rectangular prisms," there's a simple formula that answers them all.

Imagine a small cube that's 1 unit on every side — like a 1-inch wooden block. That cube has a volume of **1 cubic inch**, written as 1 in³.\n\nTo find the volume of a bigger shape, you count how many unit cubes fit inside it.\n\nBox example: a box is 3 inches long, 2 inches wide, and 4 inches tall.\n\nYou can fit 3 × 2 = 6 cubes on the bottom layer. There are 4 layers tall, so: 6 × 4 = **24 cubes**. The volume is 24 cubic inches (24 in³).

For a rectangular prism (box shape):\n\n**V = length × width × height**\n\nOr just: V = l × w × h\n\nYou can multiply in any order. A box 3 × 2 × 4 has the same volume as 4 × 3 × 2 or 2 × 4 × 3 — it's 24 either way.\n\nFor a cube (all sides equal): V = s × s × s = s³.

Volume is always measured in **cubic units**:\n\n- cubic inches (in³)\n- cubic feet (ft³)\n- cubic centimeters (cm³)\n- cubic meters (m³)\n\nAlways match your units. If the length is in feet but the width is in inches, convert first! You can't multiply them directly or your answer will be nonsense.\n\n1 cubic foot = 12 × 12 × 12 = 1,728 cubic inches (that's a lot of cubic inches in one cubic foot!).

What if a shape isn't a simple box? You can sometimes break it into smaller boxes, find the volume of each, and add them up.\n\nExample: an L-shaped object made of two rectangular prisms.\n\nPart 1: 4 × 2 × 3 = 24\nPart 2: 2 × 2 × 3 = 12\nTotal volume: 24 + 12 = **36 cubic units**\n\nThis "break it apart and add" trick works for any shape made of rectangular prisms. It's called **composite volume**.

Volume comes up everywhere — shipping, cooking, swimming pools, packing, 3D printing. Knowing how to calculate it lets you solve real problems. And once you've mastered boxes, you can tackle cylinders, pyramids, and spheres in later grades using the same idea: measure the space inside.