Volume Equations for Shapes

Common Volume Formulas:

\[ V = L \times W \times H \text{ (rectangular)} \] \[ V = \pi \times r^2 \times h \text{ (cylindrical)} \]

Select Shape:

Length:

Width:

Height:

Volume:

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1. What are Volume Equations for Shapes?

Definition: Mathematical formulas to calculate the space occupied by three-dimensional objects.

Purpose: Essential for engineering, construction, manufacturing, and any field requiring spatial measurements.

2. Common Volume Formulas

The calculator supports these fundamental formulas:

Rectangular Prism: \[ V = L \times W \times H \]
Cylinder: \[ V = \pi \times r^2 \times h \]
Sphere: \[ V = \frac{4}{3} \times \pi \times r^3 \]

Where:

\( V \) — Volume (cubic units)
\( L \) — Length (any units)
\( W \) — Width (any units)
\( H \) — Height (any units)
\( r \) — Radius (any units)
\( h \) — Height (any units)

3. Importance of Volume Calculations

Applications: Material estimation, container capacity, structural design, fluid dynamics, and more.

4. Using the Calculator

Steps:

Select the shape from the dropdown
Enter the required dimensions
Click Calculate to get the volume

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Use consistent units (all in meters, feet, etc.). The result will be in cubic units of your input.

Q2: How precise are the calculations?
A: Results are accurate to 3 decimal places. π is calculated with PHP's built-in pi() function.

Q3: Can I calculate irregular shapes?
A: This calculator handles standard shapes only. Irregular shapes require different methods.

Q4: Why doesn't the sphere have height?
A: Spheres are perfectly symmetrical - only the radius determines their volume.

Q5: How do I convert between units?
A: Convert all dimensions to the same unit before calculation (e.g., convert inches to feet).