Cone Volume Calculator: Formula, Surface Area and Step-by-Step Answer
Geometry & trigFreeNo sign-up
Enter the base radius and height of the cone.
A cone with base radius 4.0000 cm and height 9.0000 cm has a volume of 150.7964 cm³, a slant height of 9.8489 cm and a total surface area of 174.0299 cm².
Show the steps
- Base area = π r² = 50.2655 cm².
- Volume = (1/3) × base area × height = (1/3) × 50.2655 × 9.0000 = 150.7964 cm³.
- Slant height = √(r² + h²) = 9.8489 cm; lateral area = π r × slant = 123.7644 cm²; total = lateral + base = 174.0299 cm².
Cone
V = (1/3) π r² h
Slant height s = √(r² + h²)
Surface area = π r s + π r²
- A cone holds exactly one third of the cylinder with the same base and height.
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
A cone has a circular base and a point at the top. Its volume is V = (1/3) π r² h, exactly one third of the cylinder with the same base and height. Use it for funnels, party hats, ice cream cones and piles of sand.
Enter the base radius and the vertical height. You get the volume, the slant height and the surface area.
How to use it
- Enter the radius of the base and the vertical height.
- Pick the unit.
- Read the volume, slant height, surface area and steps.
Cone formulas
- Volume: V = (1/3) π r² h
- Slant height: s = √(r² + h²)
- Surface area: π r s + π r²
Example
A cone with radius 4 and height 9 has base area 50.27, so V = 50.27 × 9 ÷ 3 = 150.80 cubic units, and slant height √(16 + 81) = 9.85.
Sources
Quick check: test yourself
A cone has radius 3 cm and height 8 cm. What is its volume to the nearest tenth?
Correct answer: 75.4 cm³. V = (1/3) π r² h.
How does a cone’s volume compare with a cylinder of the same base and height?
Correct answer: One third. The cone is exactly one third of the cylinder.
A cone has radius 3 and height 4. What is its slant height?
Correct answer: 5. √(3² + 4²) = √25 = 5.
Pick an answer for each question.
Common questions
How do I find the volume of a cone?
Multiply π r² by the height, then divide by 3.
What is the slant height?
The distance along the side from the tip to the edge of the base, √(r² + h²).
Is the height the slant height?
No. Use the vertical height, straight from the tip to the center of the base.
Why divide by 3?
A cone fills one third of the cylinder with the same base and height.
What is the surface area of a cone?
The lateral area π r s plus the base area π r².
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