Continued Fraction Calculator

Calculate continued fraction metrics, mathematical formulas, and scientific computation parameters with ease.

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Mathematical Inputs

Enter matrix values, vector coordinates, radius, or derivatives.

Primary Dimension (r / x₁)

Secondary Dimension (h / y₁)

314.16 Cubic Units Volume Result for r=5, h=12

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The dot product of two orthogonal (perpendicular) vectors is always equal to zero (A · B = 0).

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Volume (V) = (1/3) × π × r² × h

Applies standard integral calculus rules and 3D solid spatial geometry identities.

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Calculations maintain 64-bit IEEE 754 precision to avoid cumulative numerical round-off error.

Follow these simple steps for exact calculation:

Enter radius r, height h, or vector component coordinates in the input fields.

The tool computes 3D volume, determinant, dot product, or surface area expansion.

Instantly view calculated output numerical value and simplified algebraic form.

Understanding 3D geometry and matrix linear algebra lays the foundation for engineering, physics, and computer graphics.

Input

Base radius r and vertical height h of 3D solid.

Output

Total enclosed 3D volume or exterior surface area.

How is the volume of a right circular cone calculated?

The volume of a cone is exactly one-third the volume of a cylinder with the same base radius and height: V = (1/3) π r² h.

What does a determinant of zero mean for a matrix?

A matrix with a determinant of zero is singular (non-invertible), meaning its rows or columns are linearly dependent and it has no matrix inverse.