A sphere is a round, three-dimensional shape.
All points on the edge of the sphere are at the same distance from the center.
The distance from the center is called the radius of the sphere. A real-world sphere is called a globe if it is large (such as the Earth), and as a ball if it is small, like an association football .
A Sphere Common things that have the shape of a sphere are basketballs, superballs, DragonBalls and playground balls.
The Earth and the Sun are nearly spherical , meaning sphere-shaped.
A sphere is the three-dimensional analog of a circle .
Calculating measures of a sphere
change
Using the circumference:
A
=
c
2
π
=
2
c
2
τ
{\displaystyle A={\frac {c^{2}}{\pi }}={\frac {2c^{2}}{\tau }}}
Using the diameter:
A
=
π
d
2
=
τ
d
2
2
{\displaystyle A=\pi d^{2}={\frac {\tau d^{2}}{2}}}
Using the radius:
A
=
2
τ
r
2
=
4
π
r
2
{\displaystyle A=2\tau r^{2}=4\pi r^{2}}
Using the volume:
A
=
3
τ
V
2
3
=
6
π
V
2
3
{\displaystyle A={\sqrt[{3}]{3\tau V^{2}}}={\sqrt[{3}]{6\pi V^{2}}}}
Using the surface area:
c
=
π
A
=
τ
A
2
{\displaystyle c={\sqrt {\pi A}}={\sqrt {\frac {\tau A}{2}}}}
Using the diameter:
c
=
π
d
=
τ
d
2
{\displaystyle c=\pi d={\frac {\tau d}{2}}}
Using the radius:
c
=
τ
r
=
2
π
r
{\displaystyle c=\tau r=2\pi r}
Using the volume:
c
=
6
π
2
V
3
=
3
τ
2
V
2
3
{\displaystyle c={\sqrt[{3}]{6\pi ^{2}V}}={\sqrt[{3}]{\frac {3\tau ^{2}V}{2}}}}
Using the surface area:
d
=
A
π
=
2
A
τ
{\displaystyle d={\sqrt {\frac {A}{\pi }}}={\sqrt {\frac {2A}{\tau }}}}
Using the circumference:
d
=
c
π
=
2
c
τ
{\displaystyle d={\frac {c}{\pi }}={\frac {2c}{\tau }}}
Using the radius:
d
=
2
r
{\displaystyle d=2r}
Using the volume:
d
=
6
V
π
3
=
12
V
τ
3
{\displaystyle d={\sqrt[{3}]{\frac {6V}{\pi }}}={\sqrt[{3}]{\frac {12V}{\tau }}}}
Using the surface area:
r
=
A
2
τ
=
A
4
π
{\displaystyle r={\sqrt {\frac {A}{2\tau }}}={\sqrt {\frac {A}{4\pi }}}}
Using the circumference:
r
=
c
τ
=
c
2
π
{\displaystyle r={\frac {c}{\tau }}={\frac {c}{2\pi }}}
Using the diameter:
r
=
d
2
{\displaystyle r={\frac {d}{2}}}
Using the volume:
r
=
3
V
2
τ
3
=
3
V
4
π
3
{\displaystyle r={\sqrt[{3}]{\frac {3V}{2\tau }}}={\sqrt[{3}]{\frac {3V}{4\pi }}}}
Using the surface area:
V
=
A
3
18
τ
=
A
3
36
π
{\displaystyle V={\sqrt {\frac {A^{3}}{18\tau }}}={\sqrt {\frac {A^{3}}{36\pi }}}}
Using the circumference:
V
=
c
3
6
π
2
=
2
c
3
3
τ
2
{\displaystyle V={\frac {c^{3}}{6\pi ^{2}}}={\frac {2c^{3}}{3\tau ^{2}}}}
Using the diameter:
V
=
π
d
3
6
=
τ
d
3
12
{\displaystyle V={\frac {\pi d^{3}}{6}}={\frac {\tau d^{3}}{12}}}
Using the radius:
V
=
2
τ
r
3
3
=
4
π
r
3
3
{\displaystyle V={\frac {2\tau r^{3}}{3}}={\frac {4\pi r^{3}}{3}}}
In Cartesian coordinates , the equation for a sphere with a center at
(
x
0
,
y
0
,
z
0
)
{\displaystyle (x_{0},y_{0},z_{0})}
(
x
−
x
0
)
2
+
(
y
−
y
0
)
2
+
(
z
−
z
0
)
2
=
r
2
{\displaystyle (x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=r^{2}}
where
r
{\displaystyle r}
![{\displaystyle A={\sqrt[{3}]{3\tau V^{2}}}={\sqrt[{3}]{6\pi V^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f89aa0867bd80472f2254e82e280570201cf8ed)
![{\displaystyle c={\sqrt[{3}]{6\pi ^{2}V}}={\sqrt[{3}]{\frac {3\tau ^{2}V}{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/098ca16739ccb4bdbb45e50169e3133b1e4edc2f)
![{\displaystyle d={\sqrt[{3}]{\frac {6V}{\pi }}}={\sqrt[{3}]{\frac {12V}{\tau }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ececc0535d245a8055e8f968e1b4212a991e76ad)
![{\displaystyle r={\sqrt[{3}]{\frac {3V}{2\tau }}}={\sqrt[{3}]{\frac {3V}{4\pi }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/14bb505c09a4461395712c7b1fdb7184196e1653)
