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Formulas for 3D Shapes Volume

Common Volume Formulas:

\[ V = L \times W \times H \text{ (rectangular)} \] \[ V = \pi \times r^2 \times h \text{ (cylindrical)} \] \[ V = \frac{4}{3} \times \pi \times r^3 \text{ (spherical)} \]

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1. What are 3D Shape Volume Formulas?

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

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

2. Common Volume Formulas

The calculator includes these fundamental formulas:

\[ V = L \times W \times H \text{ (rectangular prism)} \] \[ V = \pi r^2 h \text{ (cylinder)} \] \[ V = \frac{4}{3} \pi r^3 \text{ (sphere)} \]

Variables:

3. Applications of Volume Calculations

Examples: Determining concrete needed for foundations, calculating tank capacities, measuring material quantities.

4. Using the Calculator

Steps:

  1. Select the shape
  2. Enter required dimensions
  3. All measurements must use consistent units
  4. Results are in cubic units of the input dimensions

5. Frequently Asked Questions (FAQ)

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

Q2: How precise are the calculations?
A: Results are accurate to 3 decimal places. π is approximated as 3.14159265359.

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

Q4: What's the difference between height and length?
A: For rectangular prisms, length is typically the longest side, height is vertical. For cylinders, height is the dimension perpendicular to the circular base.

Q5: How do I convert between different cubic units?
A: Use our Unit Converter tool or multiply by conversion factors (e.g., 1 cubic meter = 35.3147 cubic feet).

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