[br][br]1) Você sabe explicar o que é o Volume de um sólido geométrico qualquer? Escreva com suas palavras.[br][br]
2) Você sabe o que é um Prisma? Descreva, com suas palavras, as características de um Prisma de base qualquer.
3) Você sabe calcular o Volume de um paralelepípedo retângulo, ou seja, o volume de um bloco retangular? Descreva uma fórmula matemática para realizar tal cálculo.
4) Na equação acima, quando se faz o produto entre o comprimento e a largura, o que de fato estamos calculando? Com base nessa resposta reescreva a fórmula anterior.
5) Você sabe explicar o Princípio de Cavalieri? Escreva com as suas palavras ou peça auxílio ao seu professor.
6) Abra o Geogebra 3D e em seguida abra o applet intitulado de “Volume do Prisma – Atividade”. Neste applet estão presentes três prismas de bases quadrangular (paralelepípedo retângulo), triangular e hexagonal, além de dois controles deslizantes denominados “Altura” e “Seção” e mais três textos na janela de álgebra que podem ser exibidos.
[br][br]7) Movimente o controle deslizante chamado de “Altura”, qual a sua funcionalidade?
8) Movimente o controle deslizante chamado “Seção”, qual sua funcionalidade?[br]
9) Os textos “Área Q”, “Área T” e “Área H” são as áreas das seções transversais vermelhas, clique sobre elas na janela de álgebra para exibi-las. O que você percebe quanto aos seus valores?
10) Ao movimentar os controles deslizantes, as áreas das seções se alteram?
11) Clique sobre a janela de visualização 3D, selecione a ferramenta 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[/img]e clique sobre cada um dos prismas para calcular seus volumes, o que você percebe sobre esses valores?
12) Considerando o Princípio de Cavalieri e as respostas das questões 9, 10 e 11, o que você pode concluir quanto aos volumes dos três prismas?
13) Conjecture uma fórmula matemática para o Volume do Prisma.