{"data":{"model":{"id":"535635","slug":"objem-kuzele","name":"Objem ku\u017eele","authorship":"author","eduProject":{"id":"2168","subject":{"id":"11","name":"Math","slug":"math","__typename":"SchoolSubjectType"},"language":{"id":"28","name":"Czech","__typename":"LanguageType"},"free":false,"timeDifficulty":"SHORT_TERM","audienceAge":"SCHOOL","complexity":"EASY","equipment":[],"suitablePrinters":[{"id":"18","name":"Prusa MINI / MINI+","__typename":"PrinterTypeType"},{"id":"5","name":"Prusa MK3 & MMU2","__typename":"PrinterTypeType"},{"id":"1","name":"Prusa MK3/S/S+","__typename":"PrinterTypeType"},{"id":"14","name":"Prusa MK3S/+ & MMU2S/3","__typename":"PrinterTypeType"}],"organisation":"Z\u00e1kladn\u00ed \u0161kola u svat\u00e9ho \u0160t\u011bp\u00e1na, Praha 2","authors":"Nat\u00e1lie Ka\u0148\u00e1kov\u00e1","targetGroupFocus":"","knowledgeAndSkills":"

Projekt je vhodn\u00fd i pro \u00fapln\u00e9 za\u010d\u00e1te\u010dn\u00edky s modelov\u00e1n\u00edm a 3D tiskem.

","objectives":"

C\u00edlem projektu je s \u017e\u00e1ky vymodelovat t\u011blesa, kter\u00e1 n\u00e1sledn\u011b vyu\u017eij\u00ed pro experiment\u00e1ln\u00ed
zji\u0161t\u011bn\u00ed objemu ku\u017eele ve srovn\u00e1n\u00ed s v\u00e1lcem se shodn\u00fdm polom\u011brem a shodnou v\u00fd\u0161kou. Ve t\u0159\u00edd\u011b mohou vzniknout t\u011blesa s r\u016fzn\u00fdmi rozm\u011bry, na \u010dem\u017e se uk\u00e1\u017ee platnost vztahu pro r\u016fzn\u00e9 velikosti. Projekt nevy\u017eaduje \u017e\u00e1dn\u00e9 p\u0159edchoz\u00ed znalosti 3D modelov\u00e1n\u00ed.

","equipmentDescription":"

B\u011b\u017en\u00e9 vybaven\u00ed IT u\u010debny, 3D tisk\u00e1rna, voda (p\u0159\u00edpadn\u011b sypk\u00fd materi\u00e1l).

","timeSchedule":"

Modelov\u00e1n\u00ed (v\u010detn\u011b instrukt\u00e1\u017ee) - 1-2 vyu\u010dovac\u00ed hodiny (podle dosavadn\u00edch zku\u0161enost\u00ed \u017e\u00e1k\u016f)
Tisk - pro vn\u011bj\u0161\u00ed polom\u011br podstavy 22 mm a v\u00fd\u0161ku 52 mm, vnit\u0159n\u00ed polom\u011br 20 mm a vnit\u0159n\u00ed v\u00fd\u0161ku 50 mm, materi\u00e1l PETG, v\u00fdpl\u0148 15 %, vrstva 0,2 mm:
\u25cf v\u00e1lec: 1 hod 23 min
\u25cf ku\u017eel: 48 min
Vyu\u017eit\u00ed v matematice - 1 hodina

","workflow":"

Postup pro tvorbu model\u016f v Tinkercad (pokyny pro studenty, pokud modelov\u00e1n\u00ed nezvl\u00e1dnou
sami):

Vytvo\u0159te v\u00e1lec s po\u017eadovan\u00fdmi vn\u011bj\u0161\u00edmi rozm\u011bry (v na\u0161em p\u0159\u00edpad\u011b pr\u016fm\u011br podstavy
44 mm, v\u00fd\u0161ka v\u00e1lce 52 mm). Aby byl v\u00e1lec co nejoblej\u0161\u00ed, zvolte nejvy\u0161\u0161\u00ed mo\u017en\u00fd po\u010det
segment\u016f (64).
Vytvo\u0159te druh\u00fd v\u00e1lec, kter\u00fd bude d\u00edrou. Jeho rozm\u011bry mus\u00ed b\u00fdt men\u0161\u00ed ne\u017e rozm\u011bry
p\u016fvodn\u00edho v\u00e1lce o po\u017eadovanou tlou\u0161\u0165ku st\u011bn. Pro st\u011bny \u0161irok\u00e9 2 mm zmen\u0161\u00edme
v\u00fd\u0161ku o 2 mm a pr\u016fm\u011br o 4 mm.
Oba v\u00e1lce zarovn\u00e1me (nap\u0159. pomoc\u00ed \u0161ipek) tak, aby st\u0159edy podstav le\u017eely na stejn\u00e9m
m\u00edst\u011b p\u0159i pohledu shora a aby v\u00e1lec-d\u00edra le\u017eel 2 mm (nebo podle zvolen\u00e9 tlou\u0161\u0165ky)
nad podlo\u017ekou.
Ozna\u010d\u00edme oba v\u00e1lce a klikneme na \u201cseskupit\u201d. Pot\u00e9 m\u016f\u017eeme z r\u016fzn\u00fdch pohled\u016f
zkontrolovat, zdali t\u011bleso vypad\u00e1 tak, jak jsme cht\u011bli. Pokud ano, objekt exportujeme do souboru .stl.
Obdobn\u011b vytvo\u0159\u00edme nejd\u0159\u00edve ku\u017eel a pot\u00e9 ku\u017eel-d\u00edru. Ku\u017eel mus\u00ed m\u00edt stejn\u00fd polom\u011br
podstavy a stejnou v\u00fd\u0161ku jako v\u00e1lec.
Op\u011bt oba ku\u017eely zarovn\u00e1me (tentokr\u00e1t budou oba le\u017eet na podlo\u017ece) a seskup\u00edme.
Po kontrole ku\u017eel exportujeme do souboru .stl.

Oba objekty importujeme do programu PrusaSlicer a nastav\u00edme podle vlastn\u00edch
po\u017eadavk\u016f. Pot\u00e9 exportujeme G-Code. Objekty m\u016f\u017eeme tisknout dohromady nebo
zvl\u00e1\u0161\u0165.

Vyu\u017eit\u00ed v hodin\u011b matematiky:

1. Ka\u017ed\u00e1 skupina (p\u0159\u00edpadn\u011b jednotlivec) dostane jeden ku\u017eel a jeden v\u00e1lec.
2. Nejprve nech\u00e1me \u017e\u00e1ky odhadnout, jak\u00fd si mysl\u00ed, \u017ee bude platit vztah pro objem v\u00e1lce a ku\u017eele se shodn\u00fdmi rozm\u011bry. Pokud se ji\u017e setkali s po\u010d\u00edt\u00e1n\u00edm objemu jehlanu, nebude pro n\u011b vztah \u201cobjem ku\u017eele = 1\u20443 objemu v\u00e1lce\u201d p\u0159ekvapen\u00edm.
3. Nyn\u00ed hypot\u00e9zu z p\u0159edchoz\u00edho bodu experiment\u00e1ln\u011b ov\u011b\u0159\u00edme. Do ku\u017eele nalejeme vodu a\u017e po okraj a n\u00e1sledn\u011b ji p\u0159elejeme do v\u00e1lce. Tento krok opakujeme, dokud nebude v\u00e1lec pln\u00fd (tj. pro spr\u00e1vn\u011b vymodelovan\u00e1 a vytisknut\u00e1 t\u011blesa 3x). P\u0159el\u00e9v\u00e1n\u00ed m\u016f\u017eeme zkusit i naopak, tj. z v\u00e1lce do ku\u017eele. Alternativn\u011b m\u016f\u017eeme m\u00edsto vody pou\u017e\u00edt nap\u0159. p\u00edsek nebo krupici. Pokud m\u00e1me ve t\u0159\u00edd\u011b v\u00e1lce a ku\u017eely r\u016fzn\u00fdch rozm\u011br\u016f, zjist\u00edme, \u017ee vztah plat\u00ed pro v\u0161echny rozm\u011bry.
4. Objemy obou t\u011bles vypo\u010d\u00edt\u00e1me. K tomu je nutn\u00e9 zm\u011b\u0159it rozm\u011bry (pokud je nezn\u00e1me z modelovac\u00ed \u010d\u00e1sti), v tomto p\u0159\u00edpad\u011b budeme m\u011b\u0159it vnit\u0159n\u00ed rozm\u011bry, vnit\u0159n\u00ed v\u00fd\u0161ku ku\u017eele m\u016f\u017eeme zm\u011b\u0159it nap\u0159\u00edklad pomoc\u00ed \u0161pejle.
5. Na z\u00e1v\u011br s \u017e\u00e1ky shrneme zji\u0161t\u011bn\u00e9 poznatky. Modely t\u011bles je mo\u017en\u00e9 nechat ve t\u0159\u00edd\u011b k dispozici pro p\u0159\u00edpad, \u017ee by n\u011bkter\u00fd z \u017e\u00e1k\u016f vztah zapomn\u011bl a pot\u0159eboval si ho p\u0159ipomenout.

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Objem kužele

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