What are the characteristics of a sphere?

In geometry, a sphere is a solid that has a completely round shape defined in three-dimensional space. Mathematically, the sphere is defined as the set of points that are located at a constant distance from a fixed point in three-dimensional space. This constant distance is called the radius and the fixed point is called the center of the sphere. An example of a sphere in real life is a ball.

Here, we will learn about the main characteristics of these geometric figures. Also, we will learn about its most used formulas and we will apply them to solve some problems.

GEOMETRY

Relevant for

Learning about the characteristics of spheres.

See characteristics

GEOMETRY

Relevant for

Learning about the characteristics of spheres.

See characteristics

Definition of a sphere

A sphere is a round geometric figure defined in three-dimensional space. The sphere is a three-dimensional solid, so it has a volume and a surface area. Similar to a circle, each point on the sphere is located the same distance from the center.

The shape of a sphere is round and has no faces. The sphere is a three-dimensional geometric figure that has a curved surface. Unlike other solids like the cube, the prism, the pyramid, a sphere does not have any flat surface. The spheres do not have vertices or edges either.

Fundamental characteristics of a sphere

The following are the fundamental characteristics of spheres:

• A sphere is perfectly symmetrical.
• Spheres are not polyhedra.
• All points on the surface of the sphere are equidistant from the center.
• Spheres do not have faces, vertices, or edges.
• The spheres have a constant mean curvature.
• They have a constant width and circumference.

Important sphere formulas

Spheres are three-dimensional figures, so their most important formulas are the volume formula and the surface area formula.

Formula for the volume of a sphere

The volume of a sphere is calculated using the length of its radius. For this, we can use the following formula:

where r represents the length of the radius of the sphere.

Formula for the surface area of a sphere

The surface area is equal to the entire outer surface of the sphere. To calculate this area, we also use the length of the radius and the following formula:

Examples of sphere problems

The formulas seen above are used to solve the following exercises.

EXAMPLE 1

What is the volume of a sphere that has a radius of 4 m?

Solution: We use the volume formula with the value $latex r=4$:

$latex V=\frac{4}{3}\pi {{r}^3}$

$latex V=\frac{4}{3}\pi {{(4)}^3}$

$latex V=\frac{4}{3}\pi (64)$

$latex V=268.1$

The volume is 268.1 m³.

EXAMPLE 2

If a sphere has a radius of 7 m, what is its volume?

Solution: We use the volume formula with $latex r=7$:

$latex V=\frac{4}{3}\pi {{r}^3}$

$latex V=\frac{4}{3}\pi {{(7)}^3}$

$latex V=\frac{4}{3}\pi (343)$

$latex V=1436.8$

The volume is 1436.8 m³.

EXAMPLE 3

A sphere has a radius of 3 m. What is its surface area?

Solution: We have the radius $latex r=3$, so we use this value in the formula for surface area:

$latex A_{s}=4\pi {{r}^2}$

$latex A_{s}=4\pi {{(3)}^2}$

$latex A_{s}=4\pi (9)$

$latex A_{s}=113.1$

The surface area is 113.1 m².

EXAMPLE 4

What is the surface area of a sphere that has a radius of 6 m?

Solution: We use the value $latex r = 6$ in the formula for surface area:

$latex A_{s}=4\pi {{r}^2}$

$latex A_{s}=4\pi {{(6)}^2}$

$latex A_{s}=4\pi (36)$

$latex A_{s}=452.4$

The surface area is 452.4 m².