Calculate the volume and surface area of 3D shapes including cubes, spheres, cylinders, cones, pyramids, and more. Choose your shape and enter dimensions.
Volume
400 cm³
Volume
400
cm³
Surface Area
340
cm²
Formula Used
V = l × w × h
| Shape | Volume Formula | Surface Area Formula |
|---|---|---|
| Cube | V = s³ | SA = 6s² |
| Rectangular Prism | V = lwh | SA = 2(lw + lh + wh) |
| Sphere | V = (4/3)πr³ | SA = 4πr² |
| Cylinder | V = πr²h | SA = 2πr(r + h) |
| Cone | V = (1/3)πr²h | SA = πr(r + √(r² + h²)) |
| Pyramid | V = (1/3)Bh | SA = B + (1/2)Ps |
| Ellipsoid | V = (4/3)πabc | SA ≈ 4π((ab^p + ac^p + bc^p)/3)^(1/p) |
Volume
400 cm³
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Volume measures 3D space. Cube: side cubed. Rectangular prism: length x width x height. Sphere: (4/3) x pi x radius cubed. Cylinder: pi x radius squared x height. Cone: (1/3) x pi x radius squared x height. Pyramid: (1/3) x base area x height. Volume is expressed in cubic units.
Volume is the measure of the three-dimensional space enclosed within a solid object. It quantifies how much space an object occupies and is expressed in cubic units such as cubic meters, cubic feet, liters, or gallons. Volume calculations are essential for engineering, construction, shipping, cooking, and many practical applications.
Volume measures 3D space. Cube: side cubed. Rectangular prism: length x width x height. Sphere: (4/3) x pi x radius cubed. Cylinder: pi x radius squared x height. Cone: (1/3) x pi x radius squared x height. Pyramid: (1/3) x base area x height. Volume is expressed in cubic units.
Volume is the amount of three-dimensional space occupied by an object. It's measured in cubic units (like cm³, m³, or ft³). Volume tells you how much a container can hold or how much space an object takes up.
Volume measures the space inside a 3D object (in cubic units), while surface area measures the total area of all the outer surfaces (in square units). For example, volume tells you how much water a box can hold, while surface area tells you how much material you need to wrap it.
Cubic units convert by cubing the linear conversion factor. For example: 1 m³ = 1,000,000 cm³ (because 100³ = 1,000,000). 1 ft³ = 1,728 in³ (because 12³ = 1,728). 1 yd³ = 27 ft³ (because 3³ = 27).
The volume of a sphere is V = (4/3)πr³, where r is the radius. This formula comes from calculus but can be visualized as being related to the volume of a cylinder with the same radius and height equal to the diameter.
A cone's volume is exactly one-third of a cylinder with the same base and height. Cone: V = (1/3)πr²h. Cylinder: V = πr²h. This 1:3 ratio holds for any cone-to-prism or pyramid-to-prism comparison.
For irregular shapes, you can: (1) Break it into regular shapes and add volumes, (2) Use water displacement method, or (3) Use calculus integration for mathematical curves. Many real objects can be approximated using combinations of basic shapes.
Last updated: 2025-01-15
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Volume
400 cm³