Select a 3D solid, enter its dimensions, and get volume and total surface area instantly with the standard formula and a worked example.
How to use this calculator
Select the 3D solid from the dropdown.
Enter the required dimensions for that shape.
Read volume and total surface area simultaneously.
Formula & method
Standard volume formulas
Sphere: V = ⁴/₃πr³ · Cylinder: V = πr²h · Cone: V = ⅓πr²h · Cube: V = s³ · Rectangular prism: V = lwh · Pyramid: V = ⅓ × BaseArea × h
r = radius, h = height, s = side, l = length, w = width.
Example
Sphere r = 5: V = (4/3)π × 125 ≈ 523.60, Surface Area = 4π × 25 ≈ 314.16.
Key insights
Tripling all linear dimensions of a 3D solid increases its volume by 3³ = 27 times (volume scales as the cube of length).
A sphere has the minimum surface area for a given volume — that is why liquids form spherical drops.
A cone has one-third the volume of a cylinder with the same base and height.
A pyramid has one-third the volume of a prism with the same base and height.
How to interpret your result
Volume vs surface area
Volume measures interior capacity (in cubic units). Surface area measures the total outside coating (in squared units). Both are important in engineering, packaging and material science.
Slant height in cones and pyramids
The slant height is the distance from the apex to the edge of the base along the surface. It differs from the perpendicular height and is needed for surface area computation.
Frequently asked questions
What is the difference between volume and capacity?
Volume is the space a solid occupies (in cm³ or m³). Capacity is the amount a hollow container can hold (in litres). 1 litre = 1000 cm³.
How do I convert cubic centimetres to litres?
Divide by 1000. For example, 500 cm³ = 0.5 litres.
What is a capsule shape?
A capsule is a cylinder with hemispherical ends — the shape of many pharmaceutical pills. Volume = πr²(⁴/₃r + h) where h is the cylinder portion length.
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