A sphere is a curved geometric body with only one rounded surface - a circular face. As a result, it does not have any edges or vertices. Edges are the segments where faces meet. Since there is only one face, they cannot be formed. In the same way, vertices cannot be created because they are the points where the edges meet, and a sphere does not have any.
Its most remarkable feature is that all its points are equidistant from the center.
According to the sphere definition, this 3D shape is a flat revolution surface generated by revolving a circle around its diameter.
A hollow sphere has the smallest area of all the surfaces that bound a given volume.
Elements and Geometric Figures of a Sphere
Center: It is the fixed point of the sphere located at the same distance from the other points of the curved surface. The center is equidistant from any surface point.
Axis: It is an infinite line that passes through the center of the geometric body.
Radius: It is the distance between the center and all sphere points.
Diameter: It is the length of the straight line that joins two points on the surface, passing through the center of which. The diameter value is twice the radius value.
Parallels are the circumferences formed by sectioning the solid by a plane perpendicular to the axis.
Meridians: They are the circumferences obtained by sectioning the sphere by a plane containing the axis.
Ecuador: is the parallel whose center coincides with the center.
What Is the Surface of a Sphere?
The formula for the surface of a sphere is:
S = 4·π·r2
“S” is the value of the surface area of the sphere expressed in square meters according to SI units.
“r” is the radius expressed in meters in the SI units.
What Is the Volume of a Sphere?
To find the volume based on the radius of the sphere, we can use the following formula:
V = (4·π·r3)/3
“V” is the volume expressed in cubic units, cubic meters in the SI units.
“r” is the radius value expressed in meters in the SI units.
Calculate the Volume of a Sphere Using a Cone and a Cylinder
To calculate the volume, we can also use the cylinder and the cone formula. The volume of the sphere is equal to 2/3 the volume of the circumscribed cylinder. On the other hand, once we have this cylinder, the volume of a cone inscribed in it is precisely one-third of the cylinder's volume.
As a result, it turns out that the sum of the volume of the cone and the sphere is equal to the cylinder's volume.
A cone has one circular face, and a cylinder has two. In both cases, these circles have the same diameter as the sphere.
Equation of the Sphere
All points X(x,y,z) of the sphere of radius r must satisfy the following equation:
If the center of the sphere is at the center of coordinates: x2 + y2 + z2 = r2.
If the center is located in the coordinates C(a,b,c) of the reference system: (x-a)2 + (y-b)2 +(z-c)2 = r2.
How to Find the Radius of a Sphere?
We have different methods to calculate the radius of a sphere depending on the initial information we have.
If we know the diameter, we can get the radius dividing by two. According to the definitions of radius and diameter, we know that radius is half the diameter, so use the formula r = d/2.
If we know the circumference (c) of the sphere's equator - its biggest flat surface section -we can use the formula r = c/2π, which comes from after isolating the radius of the circumference formula: 2πr.
In case we have the volume of a sphere, we can use the following formula r=((V/π)(3/4))(⅓). The volume of a sphere is derived from the formula of the volume of the sphere: 4/3 π·r3.
Finally, if we have the sphere surface area, we can use the formula r = √(S/(4π)).