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
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
Volume
Amount of space inside the cone
V = (1/3)πr²h
Surface Area
Total area of all surfaces
A = πr² + πr√(r²+h²)
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