Cone Volume Calculator – Guide & Formulas
Calculate the volume, slant height, and surface area of a right circular cone. Features complete formula breakdowns and step computations.
Determine the three-dimensional capacity of a cone. Perfect for measuring funnel capacities, conical pile volumes, and ice cream cones.
Key Takeaway
Use the free Cone Volume Calculator to calculate the volume, slant height, and surface area of a right circular cone. features complete formula breakdowns and step computations. Get instant results with step-by-step explanations.
How to Use the Cone Volume Calculator
- Enter the base radius or diameter of the cone.
- Enter the vertical height of the cone.
- Check the computed volume, slant height, and surface areas.
The Formula
Variable Definitions
- V: Volume of the cone
- r: Radius of the circular base
- h: Vertical height of the cone
- s: Slant height (distance from outer rim to apex)
Volume of a Sand Pile
A conical pile of road sand has a base radius of 6 feet and a height of 8 feet. Find its total sand volume.
- Step 1: Input radius r = 6 ft and height h = 8 ft.
- Step 2: Square the radius: 6² = 36.
- Step 3: Apply the volume formula: (1/3) * π * 36 * 8 = 96π ≈ 301.59 cubic feet.
- Step 4: The sand pile volume is approximately 301.59 cubic feet.
Frequently Asked Questions
Why is a cone's volume exactly 1/3 of a cylinder's?
For a cone and cylinder with the same base radius and height, calculus proves that the cone contains exactly one-third of the space. Visualizing three cones filling one cylinder helps grasp this relationship.
What is the slant height of a cone?
Slant height is the length of a straight line along the outer surface from the base perimeter up to the top apex point, solved using the Pythagorean theorem.
How do you calculate a cone's lateral surface area?
The lateral surface area is calculated with the formula A = π * r * s, where s is the slant height.