Tazama chanzo cha Tufe

[[File:Sphere wireframe 10deg 3r.svg|right|thumb|150px|Picha ya tufe]]
[[Picha:Sphere and Ball.png|thumbnail|Rediasi au nusukipenyo (= r) cha tufe]]

'''Tufe''' ni umbo la gimba linalofanana na mpira au chungwa. Lakini wala mpira wala chungwa ni tufe kamili.
 
Katika elimu ya [[hisabati]], hasa [[jiometri]] tufe ni jumla la nukta zote zilizopo na umbali uleule (=rediasi, [[nusukipenyo]]) kutoka nukta nukta moja (kitovu cha tufe).

Tufe ni mzunguko wa [[duara]] katika [[wanda]] (dimension) la tatu.

*Kitovu cha tufe ni nukta iliyopo katikati yake yenye umbali sawa na kila nukta kwenye uso wake.
*Nusukipenyo cha tufe ni umbali kati ya kitovu chake hadi nukta yoyote kwenye uso wake
*Uso wa tufe ni eneo linalojumlisha nukta zote zenye umbali wa nusukipenyo kutoka kitovu


== Mjao/v ==

Mjao wa tufe (=V) unaelezwa kwa fomula ifuatayo: 

:<math>\!V = \frac{4}{3}\pi r^3</math>

[[Pi (namba)|<math>\pi</math> (tamka pi)]] ni namba ya duara inayolingana takriban na 3.1416.Pi inaweza kukadiriwa na kuwa 3.14/²²/7.

==Eneo la uso wa tufe==

Eneo la uso wa tufe (=A) hukadiriwa kufuatana na fomula ifuatayo:

:<math>\!A =4 \pi r^2</math>

==Viungo vya Nje==
*[http://www.mathsisfun.com/geometry/sphere.html Spheres (math is fun)]
*[http://scienceforkids.kidipede.com/math/geometry/sphere.htm Sphere (scienceforkids)] {{Wayback|url=http://scienceforkids.kidipede.com/math/geometry/sphere.htm |date=20150426032329 }}
*[http://www.kidsmathgamesonline.com/facts/geometry/spheres.html Sphere facts (kidsmathgame)]
*[http://study.com/academy/lesson/sphere-definition-formulas-quiz.html Sphere: Definition, Formulas & Quiz]
*[https://www.precisionballs.com/all_wias2.php What is a Sphere? How Are Spheres Made?]
*[[planetmath:186|Sphere (PlanetMath.org website)]]
*[http://en.wikibooks.org/wiki/Mathematica/Uniform_Spherical_Distribution Mathematica/Uniform Spherical Distribution]
*{{cite video
|title=Outside In
|url=http://video.google.com/videoplay?docid=-6626464599825291409
|date=2007-11-14
|accessdate=2007-11-24
|archivedate=2007-09-01
|archiveurl=https://web.archive.org/web/20070901111142/http://video.google.com/videoplay?docid=-6626464599825291409
|deadurl=yes
}} (computer animation showing how the inside of a sphere can turn outside.)
*[http://www.start2code.com/Cresources/sphere-program-cpp.html Program in C++ to draw a sphere using parametric equation]
*[http://mathschallenge.net/index.php?section=faq&ref=geometry/surface_sphere Surface area of sphere proof.]

[[Category:Jiometria]]