Volume and 3D Shapes
Volume measures how much 3D space a solid object takes up. It is measured in cubic units (cm³, ft³, in³). The most common shape is the rectangular prism (box): volume = length × width × height. Understanding volume helps with packing boxes, filling tanks, and building structures.
Key Concepts
Volume of Rectangular Prisms
V = l × w × h. A box 4 cm × 3 cm × 5 cm = 60 cm³. You can think of it as the base area (l × w) stacked h times high. Doubling any one dimension doubles the volume; doubling all three dimensions multiplies volume by 8.
Volume of Other Shapes
Cube: V = s³. Cylinder: V = π × r² × h (the circle base times height). Cone: V = ⅓ × π × r² × h. Pyramid: V = ⅓ × base area × h. The ⅓ for cones and pyramids makes sense intuitively: three cones fill one cylinder of the same base and height.
Surface Area vs. Volume
Surface area is the total area of all faces — it tells you how much material to wrap around something. Volume tells you how much fits inside. A cube doubled in size has 4× the surface area but 8× the volume. This 'surface area to volume ratio' is important in biology, engineering, and cooking.
🆕 3D Volume Builder
Adjust dimensions and watch the volume change live!
✅ Check Your Understanding
1. Volume of a box is calculated as...
2. What are the units for volume?
3. A cube with side length 4 cm has volume...