Volume of a 3D Shape Formula

Volume Formulas:

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

Select Shape:

Length:

units

Width:

units

Height:

units

Volume:

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1. What is Volume of a 3D Shape?

Definition: Volume is the amount of space occupied by a three-dimensional object, measured in cubic units.

Purpose: Calculating volume is essential in construction, manufacturing, packaging, and many scientific applications.

2. How Does the Calculator Work?

The calculator uses different formulas based on the selected shape:

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

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 are crucial for material estimation, capacity planning, and design specifications in various industries.

4. Using the Calculator

Tips: Select the shape, enter the required dimensions (all values 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, inches, etc.). The result will be in cubic units of your input.

Q2: How do I calculate volume for irregular shapes?
A: For complex shapes, use the displacement method or break them down into regular shapes.

Q3: What's the difference between volume and capacity?
A: Volume is the total space, while capacity refers to how much a container can hold.

Q4: Why is π used in circular shape formulas?
A: π (pi) is the ratio of a circle's circumference to its diameter, essential in circular calculations.

Q5: How accurate are these calculations?
A: They're mathematically precise for perfect geometric shapes. Real-world objects may vary slightly.