Volume Calculator
Calculate the volume of cubes, spheres, cylinders, cones, and other 3D geometric shapes.
Sphere
V = (4/3)πr³
Volume Formulas
- Sphere: V = (4/3)πr³
- Cube: V = s³
- Cylinder: V = πr²h
- Cone: V = (1/3)πr²h
- Rect. Prism: V = l × w × h
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How to Use This Calculator
- Select the 3D shape you want to calculate volume for (sphere, cube, cylinder, cone, or rectangular prism)
- Enter the required dimensions: radius for sphere, side for cube, radius and height for cylinder/cone, or length, width, and height for rectangular prism
- Click Calculate to compute the volume in cubic units
- The result shows the volume based on the formula specific to your selected shape
Formula
Sphere: V = (4/3)πr³ | Cube: V = s³ | Cylinder: V = πr²h | Cone: V = (1/3)πr²h | Rectangular Prism: V = l×w×h
Frequently Asked Questions
What is volume?▼
Volume measures the amount of three-dimensional space occupied by an object, expressed in cubic units (e.g., cubic meters, cubic feet).
Why is the cone volume 1/3 of a cylinder?▼
A cone with the same base and height as a cylinder occupies exactly one-third of the cylinder's volume. This relationship can be proven using calculus or by filling a cone with water three times to fill a cylinder.
How is sphere volume derived?▼
The sphere volume formula V = (4/3)πr³ is derived using integral calculus by rotating a circle around its diameter. The 4/3 factor comes from this integration.
What's the difference between volume and surface area?▼
Volume measures the space inside a 3D object (cubic units), while surface area measures the total area of all outer surfaces (square units).