Solidi di rotazione con Geogebra IL CONO

Ciao a tutti, oggi vedremo una rapida serie di passaggi per realizzare un solido d rotazione col programma di matematica dinamica e geometria “Geogebra”.

Ecco i link per scaricare Geogebra in caso ancora non lo abbiate

Nello specifico vedremo la costruzione di un “CONO”
per chi già avesse letto quella del cilindro sarà ancor più facile, infatti le due si assomigliano… ma passaimo ora alla pretica…:

la situazione finale sarà più o meno così…

  1. definire nella barra di inserimento (in basso) la retta “f” => f(x)=x/5  => la retta “f”, in funzione della variabile “x” passa per l’ origine degli assi
  2. definire nella barra di inserimento (in basso) la retta “g” => g(x)=-(x/5)  => la retta “g”, in funzione della variabile “x” passa per l’ origine degli assi
  3. utilizzare l’ oggetto “slider” per creare una slider, di nome “retta” che utilizzeremo successivamente; con i valori:     Nome= retta     minimo= 0     massimo= 5      incremento=0.5
  4. utilizzare l’ oggetto “slider” per creare una slider, di nome “retta2″ che utilizzeremo successivamente; con i valori:     Nome= retta2     minimo= 5     massimo= 10     incremento=0.5
  5. utilizzare l’ oggetto “slider” per creare una slider, di nome “h” che utilizzeremo successivamente come variabile di supporto; con i valori:    Nome=h    minimo= 0    massimo=255    incremento=1
  6. definire ora il punto “A” nella barra di inserimento (in basso),vincolato dalla slider “retta” e sulla retta delle ascisse, =>  A=(retta,0)
  7. definire ora il punto “B” nella barra di inserimento (in basso),vincolato dalla slider “retta2″ e sulla retta delle ascisse, =>  B=(retta2,0)
  8. definire ora la circonferenza di centro “B” , vincolata quindi anch’ essa dalla slider “rett2″ => c= circonferenza[(retta2,0),f(retta2)]
  9. definire ora la circonferenza di centro “A” , vincolata quindi anch’ essa dalla slider “retta” => d= circonferenza[(retta,0),f(retta)]
  10. utilizzare l’ oggetto “slider” per creare una slider, di nome “α” che utilizzeremo successivamente come variabile di supporto nella rotazione del cono; con i valori:    Nome=α    minimo= 0°    massimo=360°    incremento=5°
  11. definire ora facoltativamente il volume del solido, dalla barra di inserimento (in basso) => V= π integrale[f(x)²,retta,retta2]

siamo ora arrivati quasi alla fine, ci manca solo di legare tramite una “lista” tutti gli elementi fin’ ora creati

nella barra di inserimento scriveremo:
lista1=Successione[Segmento[Ruota[(retta,f(retta)),α,A],Ruota[(retta2,f(retta2)),α,B]],f,1,h]

 

Buon Divertimento

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