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$$V = \frac{4}{3} \pi {r}^{3}$$
Volume
$$r = \sqrt[3]{\frac{3 V}{4 \pi}}$$
Radius
$$S_{tot} = 4 \pi {r}^{2}$$
Total surface
$$r = \sqrt{\frac{S_{tot}}{4 \pi}}$$
Radius
$$A = \pi {r}^{2}$$
Area
$$r = \sqrt{\frac{A}{\pi}}$$
Radius
$$C = 2 \pi r$$
Circumference
$$r = \frac{C}{2\pi}$$
Radius
$$d = 2r$$
Diameter
$$r = \frac{d}{2}$$
Radius
Definition
A sphere is a solid made up from all points with a distance equal or less than a costant distance, called radius of the sphere, from a fixed point, called center of the sphere.
Properties
- The sphere is a solid generated from the rotation of a semicircle around its diameter
- Radius: any segment that extends from the center of the sphere to a any point of the spherical surface
- Pi (symbol $\pi$) constant value approximated as $$\pi \simeq 3.14$$
- All the Circle formulas are valid
Sphere Formulas
| Data | Formula |
|---|---|
| Volume | V = 4/3 × π × r3 |
| Radius | V = 3√[(3V) / (4π)] |
| Total surface | Stot = 4 × π × r2 |
| Radius | r = √[Slat / (4π)] |
| Area | A = πr2 |
| Radius | r = √(A / π) |
| Circumference | C = 2πr |
| Radius | r = C / (2π) |
| Diameter | d = 2r |
| Radius | r = d/2 |