Explanation
Sphere measurements
Calculate the volume inside a sphere, its exterior surface area, or its diameter from radius. These operations distinguish cubic space from a curved two-dimensional surface.
V = 4πr³ ÷ 3
| r | Radius (m) |
|---|
Volume of a sphere with radius 3 m
| Radius | 3 |
|---|---|
| Result | 113.1 m³ |
V = 4πr³ ÷ 3 = 4π × (3 m)³ ÷ 3 = 113.0973355292 m³
S = 4πr²
| r | Radius (m) |
|---|
Surface area of a sphere with radius 3 m
| Radius | 3 |
|---|---|
| Result | 113.1 m² |
S = 4πr² = 4π × (3 m)² = 113.0973355292 m²
d = 2r
| r | Radius (m) |
|---|
Diameter of a sphere with radius 3 m
| Radius | 3 |
|---|---|
| Result | 6 m |
d = 2r = 2 × 3 m = 6 m
Diagram of this result
The sphere shows its radius from the centre along the equator. The shaded body, the heavy outline or the line through the centre marks the volume, surface area or diameter.
The sphere shows its radius from the centre along the equator. The shaded body, the heavy outline or the line through the centre marks the volume, surface area or diameter.
Common mistakes
A sphere has no flat base and uses neither cylinder height nor a circle’s planar area as its surface. The diameter crosses the whole sphere through its centre, while radius reaches only from centre to surface.
Assumptions and limits
The shape is an ideal Euclidean sphere with positive radius. Volume 4πr³/3 and surface 4πr² are finite-precision approximations; diameter 2r does not use π. Wall thickness and hollow interiors are not modelled. Canonical inputs are limited to 30 significant digits, 256 characters and adjusted exponent magnitude 100. Computation uses 50 significant digits without intermediate presentation rounding; output overflow fails explicitly. Approximate fixtures use absolute tolerance 1e-12 plus relative tolerance 1e-12.
How do the three measurements relate?
A radius of 3 m gives volume 36π m³ and surface 36π m². The numeric coefficients match for this radius, but the physical quantities and units are different. Diameter is 6 m.
Sources
Standard Euclidean measurement formulas: OpenStax Prealgebra 2e, measurement and geometry topics, https://openstax.org/details/books/prealgebra-2e. Worked examples use independent geometric identities.