Volume Calculator
• Cube: V = s³
• Rectangular Prism: V = l × w × h
• Sphere: V = (4/3)πr³
• Cylinder: V = πr²h
• Cone: V = (1/3)πr²h
• Pyramid: V = (1/3) × base area × height
Volume = π × 3² × 10
= 3.14159 × 9 × 10
= 282.74 cm³
≈ 0.28 liters
🔗 Related Calculators
📐 Formula
• Cube: V = s³
• Rectangular Prism: V = l × w × h
• Sphere: V = (4/3)πr³
• Cylinder: V = πr²h
• Cone: V = (1/3)πr²h
• Pyramid: V = (1/3) × base area × height
📝 Example Calculation
Volume = π × 3² × 10
= 3.14159 × 9 × 10
= 282.74 cm³
≈ 0.28 liters
About Volume
Volume is a fundamental measurement in geometry that quantifies the three-dimensional space occupied by a solid object. Understanding volume is crucial for many practical applications, from construction and engineering to cooking and medicine. This calculator provides volume and surface area for common 3D shapes.
Volume Formulas by Shape
- Cube: V = a^3 (where a is the side length)
- Rectangular Prism: V = l * w * h
- Sphere: V = (4/3)PIr^3
- Cylinder: V = PIr^2h
- Cone: V = (1/3)PIr^2h
- Square Pyramid: V = (1/3)a^2h
- Hemisphere: V = (2/3)PIr^3
- Ellipsoid: V = (4/3)PIabc
- Torus: V = 2PI^2Rr^2
How to Use This Calculator
- Select the 3D shape from the dropdown menu
- Enter the required dimensions for that shape
- Click "Calculate" to get the volume
- View detailed results including surface area and other properties
Understanding Volume Units
Volume is always measured in cubic units because it represents three-dimensional space. Common units include cubic meters (m^3), cubic centimeters (cm^3), cubic feet (ft^3), and cubic inches (in^3). For liquids, we often use liters, gallons, or milliliters, which are also volume measurements.
Frequently Asked Questions
What is volume?
Volume is the amount of three-dimensional space occupied by an object or enclosed within a container. It represents the capacity of a 3D shape and is measured in cubic units (like cubic meters, cubic feet, liters, or gallons).
What is the difference between volume and capacity?
Volume refers to the amount of space an object occupies, while capacity refers to the amount a container can hold. Volume is typically measured in cubic units, while capacity is often measured in units like liters, gallons, or milliliters. For a hollow container, volume refers to the material, capacity refers to what it can hold.
How do you calculate the volume of a cube?
The volume of a cube is calculated using the formula V = a^3, where a is the length of one side. Since all sides of a cube are equal, you simply cube the side length. For example, a cube with 5-unit sides has a volume of 5^3 = 125 cubic units.
What is the volume formula for a sphere?
The volume of a sphere is V = (4/3)PIr^3, where r is the radius. This can also be written as V = (4/3) * PI * r * r * r. A sphere has the smallest surface area for a given volume of any 3D shape.
How do you convert between volume units?
To convert between volume units, use conversion factors. For example: 1 cubic meter = 1,000 liters = 1,000,000 cubic centimeters; 1 cubic foot = 7.48 gallons = 28.32 liters. For cubic units, remember to cube the linear conversion factor (e.g., 1 m = 100 cm, so 1 m^3 = 100^3 = 1,000,000 cm^3).
What are real-world applications of volume calculations?
Volume calculations are used for determining container capacities, calculating concrete needed for construction, measuring medication dosages, designing fuel tanks, calculating shipping costs, determining pool water volume for chemical treatment, sizing storage spaces, and many engineering and manufacturing applications.