The sphere in spatial geometry

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THE spatial geometry it is the part of geometry that studies figures in space, that is, in three dimensions.

Three-dimensional figures are also called Geometric solids and are classified into two groups: polyhedra and round bodies.

THE ball is one of the round bodies of spatial geometry, as well as cone and cylinder.

Several objects or things that exist have the shape of a sphere, starting with the planet we live on, the Earth.

Thus, the study of sphere in spatial geometry is of great importance and with applications in several areas of knowledge.

Sphere - Spatial geometric figure

Consider a point O in space and all points that are the same distance r from that point, in all directions.

The surface formed by this set of points is called spherical surface. The spherical surface and its entire interior constitute a sphere.

Take, for example, a watermelon. The watermelon rind is the spherical surface and the whole watermelon is the sphere.

Another way to define the sphere is as the geometric figure that is formed by rotating a semicircle around its axis.

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The main formulas for the sphere are surface area and volume.

sphere area

The spherical surface area corresponds to its surface measurement and can be obtained by the following formula:

$\dpi{120} \mathbf{A = 4 \boldsymbol{\pi} r^2}$

On what:

$\dpi{120} \boldsymbol{\pi} \simeq 3.14$ ;
$\dpi{120} \mathbf{r}$ : radius of the sphere.

Sphere Volume

O sphere volume corresponds to the space occupied by it and can be calculated with the following formula:

$\dpi{120} \mathbf{V = \frac{4 \boldsymbol{\pi} r^3}{3}}$

On what:

$\dpi{120} \boldsymbol{\pi} \simeq 3.14$ ;
$\dpi{120} \mathbf{r}$ : radius of the sphere.

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