Cone & Frustum of Cone Calculator

Cone    Round platform

Number of effective digits>>>

Cone volume = (π • r² • h) / 3 Lateral area = (π • r • slant height)

Frustum

Do you know cone? If you remove the top point horizontally, it will be a truncated cone. It should be a cylinder. The top view is two circles nested, and the front view is a trapezoid.

Let the radius of the upper base be r, the radius of the lower base be R, and the height be h

Then V＝ (1/3)*π*h*(R^2 + Rr +r^2)

The volume of the truncated cone = (π • height • (Ra^2 + Ra • Rb + Rb^2) / 3)

Side area = (π • (Ra + Rb) • slant height)

A Cone & Frustum of Cone Calculator is a tool used to calculate the volume, surface area, or other properties of a cone or a frustum of a cone. These shapes are common in geometry and have practical applications in various fields such as engineering, architecture, and manufacturing. The calculator can help determine how much material is needed to create a cone or a frustum, or how much space they can occupy.

What is a Cone and a Frustum of a Cone?

  • Cone: A cone is a three-dimensional geometric shape with a circular base and a pointed top (apex) that connects to the center of the base. The sides of the cone are curved, and it tapers from the base to the apex.

  • Frustum of a Cone: A frustum is a "truncated" cone, meaning it is formed by cutting a cone horizontally. This creates a shape with two circular bases, one smaller than the other, and a slanted surface connecting the two bases.

Why Use a Cone & Frustum of Cone Calculator?

A Cone & Frustum of Cone Calculator is useful because it allows you to quickly and accurately calculate the volume, surface area, and other dimensions of these shapes, which is essential in various contexts:

  • Volume Calculation: To determine how much space is occupied by a cone or frustum. This can be useful for storing liquids, designing conical tanks, or calculating material quantities.
  • Surface Area Calculation: To find the total surface area of a cone or frustum. This is important in manufacturing, packaging, or designing conical structures.
  • Design and Engineering: For creating cones or frustums in architectural designs, engineering models, or even in 3D printing.

When to Use a Cone & Frustum of Cone Calculator?

You would use a Cone & Frustum of Cone Calculator in various scenarios:

  • Manufacturing: To calculate the volume or surface area of conical or frustum-shaped objects, such as conical tanks, funnels, and other industrial components.
  • Packaging: For determining how much material is required to create a cone or frustum-shaped container, or how much material it can hold.
  • Engineering and Architecture: When designing structures with conical shapes, like domes, spires, or towers, or calculating the amount of space needed for storage.
  • Mathematics: When solving geometry problems related to cones and frustums, such as in education or research.
  • Real-World Applications: For tasks like estimating the volume of liquids in a conical tank, or determining the surface area for painting a cone-shaped object.