1. What are Volume Formulas for 3D Shapes?

Definition: Mathematical equations used 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

Rectangular Prism: \( V = L \times W \times H \)

Cylinder: \( V = \pi \times r^2 \times h \)

Sphere: \( V = \frac{4}{3} \pi r^3 \)

Cone: \( V = \frac{1}{3} \pi r^2 h \)

3. Importance of Volume Calculations

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

4. Using the Calculator

Steps: Select shape, enter required dimensions (all must be > 0), and click Calculate.

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. For π we use PHP's pi() function (about 15 digits).

Q3: Can I calculate irregular shapes?
A: No, this calculator is for regular geometric shapes only.

Q4: Why does the form change when I select different shapes?
A: Different shapes require different dimensions (sphere needs only radius, cylinder needs radius and height, etc.).

Q5: How do I convert between units?
A: Convert all measurements to the same unit before calculation (e.g., 1 foot = 0.3048 meters).