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Volume Calculator

Calculate volume and surface area for 3D shapes
Sphere
Cube
Rect. Prism
Cylinder
Cone
Pyramid

Select a shape and enter dimensions to calculate volume.

3D Volume Formulas Guide

What is Volume?

**Volume** is the amount of three-dimensional space occupied by an object or enclosed within a container. It's measured in cubic units (e.g., cubic meters, cubic feet, cubic centimeters).

Common 3D Shapes

1. Sphere

Formula: V = (4/3)πr³

A perfectly round 3D object. Examples: basketball, globe, bubble.

2. Cube

Formula: V = a³

A 3D square with all sides equal. Examples: dice, Rubik's cube, box.

3. Rectangular Prism

Formula: V = l × w × h

A box shape with rectangular faces. Examples: book, brick, room.

4. Cylinder

Formula: V = πr²h

A circular prism. Examples: can, pipe, drum.

5. Cone

Formula: V = (1/3)πr²h

A circular base tapering to a point. Examples: ice cream cone, traffic cone.

6. Pyramid

Formula: V = (1/3) × base_area × h

A polygonal base with triangular faces meeting at apex. Examples: Egyptian pyramids, tent.

Real-World Applications

  • Architecture: Calculate material needed for construction
  • Shipping: Determine package sizes and freight costs
  • Manufacturing: Design product dimensions and packaging
  • Science: Measure liquid volumes, gas containers, etc.
Quick Tips
  • Unit Consistency
    Always use the same units for all dimensions (e.g., all in meters or all in feet).
  • π Value
    Use π ≈ 3.14159 for accurate calculations. Our calculator uses the precise value.
  • Volume vs Area
    Volume is 3D (cubic units), surface area is 2D (square units).
Common Conversions
  • 1 m³ = 1,000 liters
  • 1 ft³ = 7.48 gallons (US)
  • 1 cm³ = 1 milliliter
  • 1 in³ = 16.387 cm³

3D Geometry

Understanding volume is essential for engineering, architecture, and everyday problem-solving. Master these formulas to excel in mathematics and real-world applications.

Shape Properties
Sphere Most efficient shape - maximum volume for minimum surface area
Cube Equal dimensions - easiest to stack and pack
Cylinder Common in containers - easy to manufacture
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Volume and 3D Geometry:

Pro Tip

When measuring irregular objects, you can use water displacement: submerge the object in water and measure the volume of water displaced. This equals the object's volume!