Volume of a Cone
Find the exact volume of a cone given its radius and height. Get instant step-by-step solutions — completely free, no signup required.
Free Volume of a Cone Calculator
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About Volume of a Cone
Find the exact volume of a cone given its radius and height. Geometry explores the properties and relationships of shapes, sizes, and dimensions. From basic triangles to 3D solids, geometric formulas are used in engineering, architecture, and physics.
Our Volume of a Cone calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any volume of a cone expression and receive a complete, verified solution with every step shown.
Volume of a Cone Formula
V = (1/3)πr²h
A cone holds exactly one third of the volume of a cylinder with the same base and height. Use the perpendicular height h from the tip to the base, not the slant height along the side.
Worked Example
Find the volume of a cone with radius 4 cm and height 9 cm
- Base area: π × 4² = 16π
- Multiply by height: 16π × 9 = 144π
- Take one third: 144π ÷ 3 = 48π
- Decimal: ≈ 150.80 cm³
Answer: 48π ≈ 150.8 cm³
Common Mistakes to Avoid
- Using the slant height in place of the vertical height.
- Forgetting the factor of 1/3.
- Using the diameter instead of the radius.
How to Use the Volume of a Cone Calculator
- 1
Type your Volume of a Cone problem into the input field above
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Press Enter or click the Solve button to run the calculation
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Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Volume of a Cone formula?
V = (1/3)πr²h. A cone holds exactly one third of the volume of a cylinder with the same base and height. Use the perpendicular height h from the tip to the base, not the slant height along the side.
Can you show a worked Volume of a Cone example?
Find the volume of a cone with radius 4 cm and height 9 cm: Base area: π × 4² = 16π; Multiply by height: 16π × 9 = 144π; Take one third: 144π ÷ 3 = 48π; Decimal: ≈ 150.80 cm³. Answer: 48π ≈ 150.8 cm³.
Is this Volume of a Cone calculator free to use?
Yes — the Volume of a Cone calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Volume of a Cone homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.