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Shape
Volume formula
Surface area formula
Sphere
V
=
4
π
r
3
3
{\displaystyle V={\frac {4\pi r^{3}}{3}}}
A
=
4
π
r
2
{\displaystyle A=4\pi r^{2}\,}
Tetrahedron
V
=
1
12
2
a
3
{\displaystyle V={\begin{matrix}{1 \over 12}\end{matrix}}{\sqrt {2}}a^{3}}
A
=
3
a
2
{\displaystyle A={\sqrt {3}}a^{2}}
Cube
V
=
a
3
{\displaystyle V=a^{3}}
A
=
6
a
2
{\displaystyle A=6a^{2}}
Octahedron
V
=
1
3
2
a
3
{\displaystyle V={\begin{matrix}{1 \over 3}\end{matrix}}{\sqrt {2}}a^{3}}
A
=
2
3
a
2
{\displaystyle A=2{\sqrt {3}}a^{2}}
Dodecahedron
V
=
1
4
(
15
+
7
5
)
a
3
{\displaystyle V={\begin{matrix}{1 \over 4}\end{matrix}}(15+7{\sqrt {5}})a^{3}}
A
=
3
25
+
10
5
a
2
{\displaystyle A=3{\sqrt {25+10{\sqrt {5}}}}a^{2}}
Icosahedron
V
=
5
12
(
3
+
5
)
a
3
{\displaystyle V={\begin{matrix}{5 \over 12}\end{matrix}}(3+{\sqrt {5}})a^{3}}
A
=
5
3
a
2
{\displaystyle A=5{\sqrt {3}}a^{2}}
