Volume measures the amount of three-dimensional space a solid object occupies, expressed in cubic units (cm³, m³, in³, ft³). The volume formula depends on the shape: rectangular prism: V = l × w × h; cylinder: V = πr²h; cone: V = ⅓πr²h; sphere: V = 4/3πr³. Volume is tested on the SAT Math section and covered in Florida MAFS geometry standards (grades 7–11).
3 dimensions multiplied. Check the reference sheet for formulas.
Volume is the measure of how much three-dimensional space an object takes up. Unlike area — which measures a flat surface in square units — volume measures the interior of a solid shape in cubic units. In Florida MAFS geometry standards (MAFS.7.G.B.6 and MAFS.912.G-GMD.1), students are expected to calculate the volume of prisms, cylinders, pyramids, cones, and spheres. These same shapes appear regularly on the SAT Math section.
The volume formula you use depends on the shape. Below are the five shapes tested in Florida MAFS geometry and on the SAT Math section — learn all five.
The SAT provides these formulas on its reference sheet: V = πr²h (cylinder), V = ⅓πr²h (cone), V = 4/3πr³ (sphere). It does NOT provide V = lwh or V = s³. Know the prism formulas cold before test day.
| MEASUREMENT SYSTEM | COMMON VOLUME UNITS | CONVERSION |
|---|---|---|
| Metric | cm³, m³, mm³, L, mL | 1 L = 1,000 cm³ |
| US Customary | in³, ft³, yd³ | 1 ft³ = 1,728 in³ |
| Fluid (liquid) | fl oz, cups, gallons | 1 gallon = 231 in³ |
| THE MISTAKE | X WRONG | ✓ CORRECT |
|---|---|---|
| Using diameter instead of radius in πr²h or 4/3πr³ | V = π(10)²(5) when r=5 was given but student used d=10 | V = π(5)²(5) = 125π · Always halve the diameter before squaring |
| Forgetting the ⅓ in the cone formula | V = πr²h (cylinder formula applied to cone) | V = ⅓πr²h · A cone holds exactly one-third of the cylinder's volume |
| Answering in square units instead of cubic units | V = 200 cm² (area units) | V = 200 cm³ · Volume always requires three dimensions = cubic units |
The volume formula depends on the shape. For a rectangular prism: V = l × w × h. For a cylinder: V = πr²h. For a cone: V = ⅓πr²h. For a sphere: V = 4/3πr³. To use any formula, identify your shape, substitute the given dimensions, and solve — expressing your answer in cubic units. Florida MAFS geometry standards cover all five shapes from grade 7 through grade 11.
Yes. The SAT Math section includes volume problems involving cylinders, cones, and spheres — and provides their formulas on the reference sheet. It does not provide the rectangular prism formula (V = lwh) or the cube formula (V = s³), so those must be memorized. SAT volume problems typically require multi-step reasoning: finding a missing dimension, comparing two volumes, or combining shapes.
Volume measures the space inside a 3D shape (cubic units: cm³, m³). Surface area measures the total outer surface of that shape (square units: cm², m²). Think of it this way: if you filled a box with water, you’re measuring volume. If you wrapped a box in wrapping paper, you’re measuring surface area. The units are the clearest way to check which you’re calculating.
Because exactly three identical cones (same base radius and height) fit inside one cylinder. This is called Cavalieri’s Principle — a concept covered in Florida MAFS.912.G-GMD.1. The relationship V_cone = ⅓ × V_cylinder is the single most important cone fact to remember, and the SAT tests it directly in “fill the cone from the cylinder” problem types.
The most effective approach has three steps: (1) memorize all five formulas by writing them from scratch daily for a week; (2) practice one worked example per shape until the substitution pattern is automatic; (3) do SAT-style multi-step problems where you must choose the correct formula before solving. InLighten Tutoring’s SAT Math program in Orlando, Winter Park, and Lake Nona structures practice sessions exactly this way for student-athletes preparing for both the SAT and Florida EOC assessments.