Volume of Cylinders, Cones, and Spheres
A free Pre-Algebra lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.
A cylinder's volume is the base area (pi r^2) times the height. A cone has 1/3 the volume of a cylinder with the same base and height. A sphere's volume is (4/3) pi r^3 — about two-thirds of the cylinder that snugly contains it (Archimedes). In Geometry Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Compute volume of a cylinder using V = pi * r^2 * h
- Compute volume of a cone using V = (1/3) * pi * r^2 * h
- Compute volume of a sphere using V = (4/3) * pi * r^3
Worked example
Problem. A cylinder has r = 3 and h = 10. Find V (pi = 3.14).
- V = pi * r^2 * h = 3.14 * 9 * 10.
- = 3.14 * 90 = 282.6.
- Connect the calculation back to Volume of Cylinders, Cones, and Spheres so the method, not just the arithmetic, is clear.
- Check the result against the original question before writing the final answer.
Answer: 282.6
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Cylinder r = 2, h = 10 (pi = 3.14).
Show solution
- V = 3.14 * 4 * 10.
- = 125.6.
Answer: 125.6
2. Cylinder r = 5, h = 4 (pi = 3.14).
Show solution
- V = 3.14 * 25 * 4.
- = 314.
Answer: 314
3. Cone r = 3, h = 10 (pi = 3.14).
Show solution
- V = (1/3) * 3.14 * 9 * 10.
- = (1/3) * 282.6 = 94.2.
Answer: 94.2
4. Cone r = 6, h = 5 (pi = 3.14).
Show solution
- V = (1/3) * 3.14 * 36 * 5.
- = (1/3) * 565.2 = 188.4.
Answer: 188.4
5. Sphere r = 3 (pi = 3.14).
Show solution
- V = (4/3) * 3.14 * 27.
- = 4 * 28.26 = 113.04.
Answer: 113.04
Practice this interactively with instant feedback and an AI tutor.
Practice Volume of Cylinders, Cones, and Spheres Take the free placement check