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ఘనపరిమాణము: కూర్పుల మధ్య తేడాలు

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విజువల్వికీటెక్స్ట్
పంక్తి 89:
!Variables
|-
|సమఘనం
|[[:en:Cube_(geometry)|Cube]]
| style="text-align:center" |<math>V=a^3\;</math>
| style="text-align:center" |[[File:Wuerfel-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Wuerfel-1-tab.svg|85x85px]]
|-
|దీర్ఘ ఘనం
|[[:en:Cuboid|Cuboid]]
| style="text-align:center" |<math>V=abc</math>
| style="text-align:center" |[[File:Quader-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Quader-1-tab.svg|150x150px]]
|-
|పట్టకం
|[[:en:Prism_(geometry)|Prism]]
(''B'': భూ వైశాల్యం )
(''B'': [[:en:Area|area]] of base)
| style="text-align:center" |<math>V=B h</math>
| style="text-align:center" |[[File:Prisma-1-e.svg|link=https://en.wikipedia.org/wiki/File:Prisma-1-e.svg|120x120px]]
|-
|(''B'': భూ వైశాల్యం )
|[[:en:Pyramid_(geometry)|Pyramid]]
(''B'': area of base)
| style="text-align:center" |<math>V=\frac{1}{3} B h</math>
| style="text-align:center" |[[File:Pyramide-46-e.svg|link=https://en.wikipedia.org/wiki/File:Pyramide-46-e.svg|200x200px]]
|-
|క్రమ టెట్రా హైడ్రన్
|[[:en:Parallelepiped|Parallelepiped]]
| style="text-align:center" |<math>V=a b c \sqrt{K}</math>{{paragraph}}<math>\begin{align}
K = 1 &+ 2\cos(\alpha)\cos(\beta)\cos(\gamma) \\
&- \cos^2(\alpha) - \cos^2(\beta) - \cos^2(\gamma)
\end{align}</math>
| style="text-align:center" |[[File:Parallelepiped-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Parallelepiped-1-tab.svg|150x150px]]
|-
|Regular [[:en:Tetrahedron|tetrahedron]]
| style="text-align:center" |<math>V={\sqrt{2}\over12}a^3 \,</math>
| style="text-align:center" |[[File:Tetraeder-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Tetraeder-1-tab.svg|100x100px]]
|-
|గోళం
|[[:en:Sphere|Sphere]]
| style="text-align:center" |<math>V=\frac{4}{3} \pi r^3 </math>
| style="text-align:center" |[[File:Kugel-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Kugel-1-tab.svg|100x100px]]
|-
|దీర్ఘ గోళం
|[[:en:Ellipsoid|Ellipsoid]]
| style="text-align:center" |<math>V=\frac{4}{3}\pi abc</math>
| style="text-align:center" |[[File:Ellipsoid-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Ellipsoid-1-tab.svg|150x150px]]
|-
|వృత్తాకార స్థూపం
|[[:en:Cylinder_(geometry)|Circular Cylinder]]
| style="text-align:center" |<math>V=\pi r^2 h</math>
| style="text-align:center" |[[File:Zylinder-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Zylinder-1-tab.svg|105x105px]]
|-
|శంకువు
|[[:en:Cone_(geometry)|Cone]]
| style="text-align:center" |<math>V=\frac{1}{3}\pi r^2 h</math>
| style="text-align:center" |[[File:Kegel-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Kegel-1-tab.svg|100x100px]]
|-
|[[:en:Solid_torus|Solid torus]]
| style="text-align:center" |<math>V=2\pi^2 Rr^2</math>
| style="text-align:center" |[[File:Torus-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Torus-1-tab.svg|200x200px]]
|-
|[[:en:Solid_of_revolution|Solid of revolution]]
| style="text-align:center" |<math>V= \pi \cdot \int_ {a}^b f(x)^2\mathrm{d}x </math>
| style="text-align:center" |[[File:Vase-1-tab.svg|link=https://en.wikipedia.org/wiki/File:Vase-1-tab.svg|220x220px]]
|-
|Solid body with continuous area
 
 
<math>A(x)</math> of its cross sections
 
(example: [[:en:Steinmetz_solid|Steinmetz solid]])
| style="text-align:center" |<math>V= \int_ {a}^b A(x)\mathrm{d}x </math>
|For the solid of revolution above:
 
 
<math>A(x)=\pi f(x)^2</math>
|}
 
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