📦 Volume — Complete SAT Math Guide
What is Volume? Volume is the amount of three-dimensional space occupied by a solid figure. It is measured in cubic units such as cm³, mm³, m³, in³, or ft³.
Volume answers two key questions:
- 🔹 "How much space does this object take up?"
- 🔹 "How much can this container hold?"
SAT Tip: The SAT provides a reference sheet with volume formulas, but knowing them by heart saves precious time. Understanding why each formula works helps you avoid common trap answers.
🧊 Interactive Graphic 1: 3D Unit Cube Builder
Use the sliders below to build a rectangular prism layer by layer. Watch how Volume = length · width · height builds up!
Interactive visualization — available in the full lesson
Controls
V = 3 · 3 · 3 = 27 cubic units
Total unit cubes: 27
📐 Rectangular Prism (Cuboid)
$$V = l \cdot w \cdot h$$
Where:
- $l$ = length
- $w$ = width
- $h$ = height
⚠️ Important: All three dimensions must be in the same units before calculating!
Example: A box with $l = 5$ cm, $w = 3$ cm, $h = 4$ cm:
$V = 5 \cdot 3 \cdot 4 = 60$ cm³
Interactive visualization — available in the full lesson
V = 5 · 3 · 4 = 60 cm³