Volume of Shapes Formulas

Volume Formulas:

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

Select Shape:

Length:

units

Width:

units

Height:

units

Volume:

cubic units

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1. What is Volume Calculation?

Definition: Volume is the amount of three-dimensional space occupied by an object or substance.

Purpose: Calculating volume is essential in construction, manufacturing, science, and everyday life for determining capacity, material quantities, and spatial requirements.

2. Common Volume Formulas

The calculator supports these formulas:

Rectangular Prism: \[ V = L \times W \times H \] Cylinder: \[ V = \pi \times r^2 \times h \]

Where:

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

3. Importance of Volume Calculation

Details: Accurate volume calculations ensure proper material estimation, structural integrity, and cost efficiency in projects.

4. Using the Calculator

Tips: Select the shape, enter the required dimensions, and click Calculate. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Use any consistent unit (meters, feet, inches), but all dimensions must be in the same unit.

Q2: How accurate are the calculations?
A: The calculations are mathematically precise based on the formulas and your input values.

Q3: Can I calculate volume for irregular shapes?
A: This calculator handles standard shapes only. For complex shapes, use specialized methods or software.

Q4: What's the value of π used?
A: We use PHP's built-in pi() function which provides ~3.1415926535898.

Q5: How do I convert between units?
A: Convert all dimensions to the same unit before calculation (e.g., 1 foot = 12 inches).