Volume de Um Prisma

[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.
Volume do Prisma
[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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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.
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Information: Volume de Um Prisma