Plano de Aula[br][br]Conteúdo: Volume do Cilindro[br]Ano: 8º Ano[br]Recursos: GeoGebra 2D e 3D[br]Habilidade:(EF08MA21) Resolver e elaborar situações- problema que envolvam o cálculo do volume de[br]recipiente cujo formato é o de um cilindro reto. [br]Número de aulas: 2 aulas[br]
O volume é a medida que corresponde a quantidade de espaço ocupado por um determinado objeto. Dito isso, o volume refere-se ao espaço interno da figura geométrica.[br]Hoje, vamos estudar o cilindro, que é um sólido do grupo dos corpos redondos, aqueles que têm superfície arredondada.[br]Um cilindro circular reto (ou simplesmente cilindro reto) é característica por duas superfícies planas e paralelas formadas por círculos idênticos, que são suas bases.[br]O segmento de reta que liga os centros das bases (círculos) do cilindro é o eixo do cilindro. Em um cilindro reto, o eixo é perpendicular aos planos das bases.[br]Logo, para podermos calcularmos o volume do cilindro precisamos da seguinte fórmula:[br][br]Volume do Cilindro[br][br][img]https://th.bing.com/th/id/OIP.fm0UVQPPA5LyNcNj9tif2gAAAA?pid=ImgDet&rs=1[/img] [img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img][br][br][br][br] [br]
Vídeo sobre o volume do cilindro e como calculá-lo.
Construção do Cilindro no GeoGebra para auxiliar nas atividades
Atividade de criação do Cilindro
1. Com o auxílio do GeoGebra, construa um cilindro e descreva o que verificou em cada caso: [br]a) com raio 2 e altura 5[br]b) com controle deslizante do raio[br]c) com controle deslizante da altura[br]d) com controle deslizante do raio e altura[br]
2. Com o auxílio do GeoGebra, construa um cilindro, calcule o volume [img]data:image/png;base64,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[/img] e descreva o que verificou em cada caso: (Gravar no GeoGebra)[br]a) com raio 2 e altura 5[br]b) com controle deslizante do raio[br]c) com controle deslizante da altura[br]d) com controle deslizante do raio e altura
3. (Vunesp) Um pedreiro deseja construir uma caixa d'água, em forma de cilindro, com capacidade para 25,12 mil litros. Considerando [img]data:image/png;base64,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[/img], para que a altura desse reservatório seja 2 metros, a medida aproximada do raio da base, em metros, deverá ser: