Volume: Cylinders, Cones & Spheres
Aligned to 8.G.C.9 — Common Core State Standards for Mathematics.
What this lesson teaches
Volume formulas: cylinder V = πr^2h, cone V = (1/3)πr^2h, and sphere V = (4/3)πr^3. A cone is exactly one-third of a cylinder that has the same base and height.
Worked examples
Example 1
Find the volume of a cylinder with radius 3 and height 5. V = πr^2h = π(3^2)(5) = π(9)(5) = 45π ≈ 141.4 cubic units.
Example 2
A cone with radius 3 and height 5 holds exactly a third of the matching cylinder: V = (1/3)π(9)(5) = 15π ≈ 47.1 cubic units.
Example 3
A sphere of radius 3: V = (4/3)π(27) = 36π ≈ 113.1 cubic units. Radius is cubed, so doubling it multiplies the volume by 8.
Practice questions
- Find the volume of a cylinder with radius 2 and height 10 (leave your answer in terms of π).
- Find the volume of a cone with radius 6 and height 9.
- Find the volume of a sphere with radius 3 (leave your answer in terms of π).
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Volumen: Cilindros, Conos y Esferas
Fórmulas de volumen: cilindro V = πr^2h, cono V = (1/3)πr^2h y esfera V = (4/3)πr^3. Un cono es exactamente un tercio de un cilindro que tiene la misma base y altura.
Ejemplo 1: Halla el volumen de un cilindro con radio 3 y altura 5. V = πr^2h = π(3^2)(5) = π(9)(5) = 45π ≈ 141.4 unidades cúbicas.
Ejemplo 2: Un cono con radio 3 y altura 5 contiene exactamente un tercio del cilindro correspondiente: V = (1/3)π(9)(5) = 15π ≈ 47.1 unidades cúbicas.
Ejemplo 3: Una esfera de radio 3: V = (4/3)π(27) = 36π ≈ 113.1 unidades cúbicas. El radio se eleva al cubo, así que duplicarlo multiplica el volumen por 8.
More Geometry lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required