Tufe

Tufe ni umbo la gimba linalofanana na mpira au chungwa. Lakini wala mpira wala chungwa ni tufe kamili.

Picha ya tufe

Rediasi au nusukipenyo (= r) cha tufe

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

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

$\!V={\frac {4}{3}}\pi r^{3}$

$\pi$ (tamka pi) ni namba ya duara inayolingana takriban na 3.1416.

Eneo la uso wa tufe

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

$\!A=4\pi r^{2}$

Viungo vya Nje

• Spheres (math is fun)
• Sphere (scienceforkids) Archived 26 Aprili 2015 at the Wayback Machine.
• Sphere facts (kidsmathgame)
• Sphere: Definition, Formulas & Quiz
• What is a Sphere? How Are Spheres Made?
• Sphere (PlanetMath.org website)
• Mathematica/Uniform Spherical Distribution
• Outside In. 2007-11-14. Archived from the original on 2007-09-01. https://web.archive.org/web/20070901111142/http://video.google.com/videoplay?docid=-6626464599825291409. Retrieved 2007-11-24. (computer animation showing how the inside of a sphere can turn outside.)
• Program in C++ to draw a sphere using parametric equation
• Surface area of sphere proof.