Cone Volume Calculator
Calculate the volume of a right circular cone given its radius and height. Perfect for determining capacities of funnels, ice cream cones, conical tanks, and other conical containers.
Calculate Cone Volume
Enter the dimensions of the cone:
V = (1/3) Γ Ο Γ radiusΒ² Γ height
Understanding Cone Volume
The cone is one of the most common three-dimensional shapes in both nature and manufactured objects. Its volume calculation is fundamental to geometry and has countless practical applications.
The Cone Volume Formula
π Basic Formula
V = (1/3)ΟrΒ²h
Volume equals one-third of Ο times radius squared times height
This is the standard formula for right circular cones
π€ Why One-Third?
A cone's volume is exactly one-third the volume of a cylinder with the same base and height
This relationship comes from the way a cone can be divided into three equal pyramids
π Surface Area
Lateral Area = Οrβ
Base Area = ΟrΒ²
Total Surface Area = Οrβ + ΟrΒ²
Where β is the slant height
π‘ Pro Tip: The slant height (β) is calculated as β = β(rΒ² + hΒ²), where r is the radius and h is the height. This is essential for calculating the lateral surface area of the cone.
Common Cone Volumes
| Object | Radius | Height | Volume | Application |
|---|---|---|---|---|
| Ice Cream Cone | 3.5 cm | 10 cm | 128.68 cmΒ³ | Food portion control |
| Kitchen Funnel | 5 cm | 15 cm | 392.70 cmΒ³ | Liquid transfer |
| Traffic Cone | 15 cm | 75 cm | 17671.46 cmΒ³ | Road safety equipment |
| Party Hat | 8 cm | 20 cm | 1340.41 cmΒ³ | Celebration supplies |
| Megaphone | 10 cm | 30 cm | 3141.59 cmΒ³ | Sound amplification |
| Small Water Tower | 2 m | 8 m | 33.51 mΒ³ | Water storage |
Cone Properties and Relationships
π Slant Height
β = β(rΒ² + hΒ²)
The slant height is the distance from the base edge to the apex along the lateral surface
Essential for surface area calculations
π Volume Ratio
Cone Volume = (1/3) Γ Cylinder Volume
Both shapes have the same base radius and height
This relationship holds for all right circular cones
π Surface Areas
Lateral Surface Area = Οrβ
Base Surface Area = ΟrΒ²
Total Surface Area = Οrβ + ΟrΒ²
Includes both curved and flat surfaces
Liquid Volume Conversions
| Cubic Volume | Liters | US Gallons | US Cups | Application |
|---|---|---|---|---|
| 1000 cmΒ³ | 1 L | 0.26 gal | 4.23 cups | Standard liter volume |
| 3785 cmΒ³ | 3.785 L | 1 gal | 16 cups | US gallon equivalent |
| 236.6 cmΒ³ | 0.237 L | 0.063 gal | 1 cup | US cup equivalent |
| 1000000 cmΒ³ | 1000 L | 264.17 gal | 4226.75 cups | Cubic meter volume |
Real-World Applications
π Industrial Uses
Conical tank capacity calculations
Funnel design specifications
Mining cone volume measurements
Mixer bowl capacity determination
Conical reactor vessel sizing
π Household Items
Ice cream cone volume measurement
Funnel capacity for liquid transfer
Party hat size specifications
Conical measuring cups
Beverage container design
π§ Construction
Traffic cone specifications
Conical pile volume calculations
Foundation cone measurements
Concrete form work calculations
Architectural cone designs
π¨ Art & Design
Conical sculpture volume planning
Lamp shade capacity calculations
3D printing cone designs
Package design specifications
Ceramic cone mold sizing
Advanced Cone Mathematics
π Frustum Volume
V = (1/3)Οh(RΒ² + Rr + rΒ²)
Where R is top radius, r is bottom radius
Used for truncated cones
Important in engineering applications
π’ Lateral Surface Area
A = Οrβ where β = β(rΒ² + hΒ²)
The curved surface area of the cone
Excludes the base area
Used in material calculations
π Cone Development
A cone can be "unrolled" into a sector of a circle
Sector angle = 360Β° Γ (base circumference / slant height)
Used in pattern making and manufacturing
Cone Volume in Different Contexts
| Context | Application | Example Calculation |
|---|---|---|
| Manufacturing | Hopper design | Conical storage bin capacity |
| Agriculture | Silo capacity | Grain storage cone volume |
| Food Industry | Portion control | Ice cream cone volume standards |
| Chemical Engineering | Reactor design | Conical reaction vessel capacity |
| Architecture | Dome calculations | Conical roof volume planning |
| 3D Printing | Material usage | Cone model volume estimation |