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Math • Cone Volume Calculator

Cone Volume Calculator

Calculate the volume and surface area of a cone from radius and height.

Volume (V = ⅓πr²h)
150.796
Total Surface Area
174.030
Slant Height (s)
9.849
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Calculation Guide & Reference

Cone Volume & Surface Area Mathematics

Cone volume calculator computes volume and surface area from radius and height, using V = (1/3)πr²h.

Standardized Mathematical Formula
V = (1/3)πr²h

A cone's volume is exactly one-third of a cylinder with the same base and height — the formula is the cylinder volume formula divided by 3.

Variables:
r:Radius of the circular base
h:Height of the cone (apex to base center)
How It Works (Step-by-Step)
  • 1Enter the radius and height of the cone.
  • 2View the volume, slant height, and total surface area.
Real-World Numerical Example
A Cone with Radius 4 and Height 9

An ice cream cone shape has a radius of 4 units and a height of 9 units.

•Base area: π × 4² = 16π.
•Volume: (1/3) × 16π × 9 = 48π ≈ 150.80 cubic units.
Result: The cone's volume is approximately 150.80 cubic units.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

V = (1/3)πr²h — one-third of the equivalent cylinder's volume (πr²h) with the same radius and height.

This is a geometric fact provable with calculus (integrating the cross-sectional area from apex to base) — it holds for any cone and its corresponding cylinder of equal base and height.

Slant height is the distance from the apex to the edge of the base along the cone's surface (√(r² + h²)) — it's needed to calculate the cone's lateral surface area, separate from its volume.

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