Cone Volume Calculator

Calculate the volume, surface area, and dimensions of regular and truncated cones

Calculate Cone Volume

Distance from center to edge of circular base

Perpendicular distance from base to apex

Cone Results

Volume

0.00
cm³
0.0000
Liters
0.000
in³
0.000000
0.0000
ft³
0.0000
Gallons
0.00 cm²
Surface Area
0.00 cm
Slant Height

Formula used: V = (1/3) × π × r² × h

Where: r = 0.00cm (radius), h = 0.00cm (height)

Calculation Analysis

Example Calculation

Ice Cream Cone

Radius: 3 cm

Height: 11 cm

Formula: V = (1/3) × π × r² × h

Calculation

V = (1/3) × π × 3² × 11

V = (1/3) × π × 9 × 11

V = (1/3) × π × 99

V = 103.67 cm³

Cone Properties

V

Volume

Amount of space inside the cone

V = (1/3)πr²h

A

Surface Area

Total area of all surfaces

A = πr² + πr√(r²+h²)

L

Slant Height

Distance from apex to base edge

L = √(r²+h²)

Quick Tips

A cone is 1/3 the volume of a cylinder with same base and height

The apex is the pointed top of the cone

Truncated cones are also called frustums

Ice cream cones and traffic cones are common examples

Understanding Cone Volume

What is a Cone?

A cone is a three-dimensional geometric shape with a circular base that tapers smoothly to a single point called the apex. The height is the perpendicular distance from the base to the apex, and the radius is the distance from the center to the edge of the base.

Types of Cones

  • Right Cone: Apex directly above the center of the base
  • Oblique Cone: Apex not directly above the center
  • Truncated Cone: Cone with the top cut off (frustum)

Volume Formula Explanation

Regular Cone: V = (1/3) × π × r² × h

Truncated Cone: V = (1/3) × π × h × (R² + R×r + r²)

  • V: Volume of the cone
  • π: Pi (approximately 3.14159)
  • r: Radius of the base (or top radius for truncated)
  • R: Base radius (for truncated cones)
  • h: Height of the cone

Remember: A cone has exactly 1/3 the volume of a cylinder with the same base and height.

Real-World Applications

Food Industry

Ice cream cones, funnel cakes, pastry bags

Construction

Traffic cones, roof designs, architectural features

Manufacturing

Hoppers, funnels, storage tanks

Science

Volcanic cones, speaker cones, laboratory equipment