Cone Volume Calculator

Calculate the volume of a cone using radius and height with our cone volume calculator. Get results with the cone volume formula and step-by-step calculations.

π setting: π = 3.14159265

π Precision:

Base Radius (r):

Perpendicular Height (h):

Cone Volume

150.7964m³

Decimals:

Step-by-Step Mathematical Solution

Formula:V = (1/3) × π × r² × h

Steps:

1.Base Radius (r) = 4 m, Height (h) = 9 m

2.Formula: V = (1/3) × π × r² × h

3.Square Radius: r² = 4² = 16

4.Multiply r² × h = 144

5.Multiply by (1/3)π ≈ 1.04719755: V ≈ 150.7964 m³

Calculated Volume:150.7964 m³

What Is a Cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat, circular base to a single point called the apex or vertex.

In a right circular cone, the line connecting the center of the circular base to the apex is perpendicular to the base plane. Traffic cones, ice cream cones, and volcano peaks are common real-world cone shapes.

Volume of a Cone Formula

Standard Formula

V = (1/3) × π × r² × h

Formula Variables Explained:

rBase Radius

The radius of the circular base of the cone.

hHeight

The perpendicular distance from the center of the base to the apex point.

sSlant Height

The length from the outer perimeter of the base circular edge to the apex.

The volume of a cone is exactly one-third the volume of a cylinder with the same circular base radius (r) and perpendicular height (h).

The general formula is V = (1/3) × π × r² × h. If you are given the slant height (s) and radius (r), you can find perpendicular height using the Pythagorean theorem: h = √(s² - r²).

How to find the volume of a Cone?

1Measure or locate the base radius (r) and perpendicular height (h).
2Square the radius: r² = r × r.
3Multiply r² by the height (h) and Pi (π).
4Divide the final result by 3 to account for the conical taper.
5Express the result in cubic measurement units (cm³, m³, in³, ft³).

Example: Calculate the Volume of a Cone

Example 1: Calculate cone volume with radius 4 m and height 9 m

Problem: A conical storage bin has a circular base radius of 4 meters and a height of 9 meters. Calculate its storage volume.

Solution Steps:

Formula: V = (1/3) × π × r² × h
Substitute r = 4 and h = 9: V = (1/3) × π × (4²) × 9
Calculate 4² = 16
V = (1/3) × π × 16 × 9
V = π × 16 × 3 = 48π
V ≈ 48 × 3.14159265 ≈ 150.80 m³

Final Volume:150.80 cubic meters

Frequently Asked Questions (FAQ)

Q: Why is a cone volume one-third of a cylinder?

Geometric calculus and Archimedes proofs show that pouring water from a cone with radius r and height h into a cylinder with identical base and height will fill exactly one-third of the cylinder.

Q: How to calculate cone volume using slant height?

First calculate perpendicular height h using Pythagorean theorem h = √(s² - r²), then plug r and h into V = (1/3)πr²h.

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