3D Volume
Sphere, cube, cylinder, cone, box
About This Calculator
Volume measures the amount of three-dimensional space enclosed by a solid shape. These formulas are essential in engineering, packaging, architecture, and any field that deals with physical objects.
Formula
Sphere: V = (4/3)*pi*r^3
Cube: V = s^3; Cylinder: V = pi*r^2*h; Cone: V = (1/3)*pi*r^2*h
Rectangular box: V = l*w*h
Example Calculation
Cylinder with radius 5 and height 10
- V = pi * r^2 * h = pi * 25 * 10
- V = 250 * pi = 785.4 cubic units
Volume = 785.40 cubic units
Volume Comparison (r=5, s=5, h=10 where applicable)
| Shape | Dimensions | Volume |
|---|---|---|
| Sphere | r=5 | 523.60 |
| Cube | s=5 | 125.00 |
| Cylinder | r=5, h=10 | 785.40 |
| Cone | r=5, h=10 | 261.80 |
| Box | 5 x 5 x 10 | 250.00 |
Frequently Asked Questions
Why does a cone have 1/3 the volume of a cylinder?
A cone with the same base radius and height as a cylinder has exactly 1/3 of the cylinder's volume. This can be proven by calculus (integration) or by filling a cone 3 times to fill the cylinder.
How do I find the volume of an irregular solid?
Use water displacement (Archimedes' method): submerge the object in a graduated container and measure how much water it displaces. The volume of displaced water equals the object's volume.
What is surface area vs. volume?
Surface area measures the total outer surface in square units; volume measures the interior space in cubic units. A sphere has the smallest surface area for a given volume — which is why bubbles are spherical.