Volume of Cylinders, Cones & Spheres

Three formulas

When you study three formulas, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

1. 1Cylinder: V = πr²h.
2. 2Cone: V = (1/3)πr²h - a third of a cylinder with the same base and height.
3. 3Sphere: V = (4/3)πr³.

Volume measures space inside a 3D object, in cubic units. Think of how many unit cubes would fill the shape.

For prisms, volume is often (area of the base) × (height). The base and height must be perpendicular for that shortcut.

Volume measures space inside a 3D object, in cubic units. Think of how many unit cubes would fill the shape.

For prisms, volume is often (area of the base) × (height). The base and height must be perpendicular for that shortcut.

Why this matters

Volume of Cylinders, Cones & Spheres shows up constantly in apply the three key volume formulas with π. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

1. Three formulas
2. Cylinder: V = πr²h.
3. Cone: V = (1/3)πr²h - a third of a cylinder with the same base and height.
4. Sphere: V = (4/3)πr³.