Volume Equations of 3D Shapes

Common Volume Formulas:

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

Select Shape:

Length (L):

Width (W):

Height (H):

Unit:

Volume:

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1. What are Volume Equations of 3D 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 shapes:

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

Where:

\( V \) — Volume (cubic units)
\( L, W, H \) — Length, Width, Height (rectangular prism)
\( r \) — Radius (cylinder/sphere)
\( h \) — Height (cylinder)
\( \pi \) — Pi (approximately 3.14159)

3. Importance of Volume Calculations

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

4. Using the Calculator

Steps:

Select the shape
Enter required dimensions
Choose measurement units
Click Calculate

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Any consistent unit (meters, feet, inches, etc.). The result will be in cubic units of your choice.

Q2: How precise are the calculations?
A: Results show 3 decimal places. For π we use PHP's M_PI constant (about 15 digits precision).

Q3: Can I calculate volumes for other shapes?
A: This calculator covers basic shapes. Other shapes like cones or pyramids would require different formulas.

Q4: Why does the input form change?
A: Different shapes require different dimensions (radius for spheres, length/width/height for rectangular prisms, etc.).

Q5: How do I convert between units?
A: Use our Unit Conversion tool or multiply by conversion factors (e.g., 1 m³ = 35.3147 ft³).