At this station, you have a collection of prisms. Cling nets are included as well.

Transcription

1 At this station, you have a collection of prisms. Cling nets are included as well. Sketch a picture of the net for a non- rectangular prism. Label the net to indicate the parts of the prism including edge, base, lateral face, vertex. Justify your labels. Using the nets, find an expression for the surface area of a prism. Record this expression in your booklet.

2 At this station, you have a collection of cylinders. Cling nets are included as well. Sketch a picture of the net for a cylinder. Label the net to indicate the parts of the cylinder including edge, base, lateral face, vertex. Justify your labels. Using the nets, find an expression for the surface area of a cylinder. Record this expression in your booklet.

3 At this station, you have a collection of pyramids. Cling nets are also included. Sketch a picture of the net for a pyramid. Label the net to indicate the parts of the pyramid including edge, base, lateral face, vertex. Justify your labels. Using the nets, find an expression for the surface area of a pyramid. Record this expression in your booklet.

4 At this station, you have a collection of cones. Cling nets are also included. Sketch a picture of the net for a cone. Label the net to indicate the parts of the cone including edge, base, lateral face, vertex. Justify your labels. Using the nets, find an expression for the surface area of a cone. Record this expression in your booklet.

5 At this station, you have a collection of spheres. Surface Area: Archimedes determined that the surface area of a sphere is equal to the lateral area of the circumscribed cylinder. Show how this will lead to a formula for the surface area of a sphere. (see Volume: Now imagine covering the sphere with tiny triangles. Construct a pyramid whose base is the tiny triangle and whose vertex is at the center of the sphere. Questions: What is the volume of this pyramid? If I were to do this over and over again, what could I call the sum of the tiny triangles which cover the sphere? How can I use that to help me determine a formula for the volume of a sphere?.

6 At this station, you have a collection of prisms and pyramids as well as rice. Using a layer analogy, write an expression for the volume of a prism. Question: For a pyramid and prism with congruent bases and congruent heights, how many pyramids do you think it will take to fill a prism? Using the rice/water, fill the pyramid. Pour this volume into the respective prism. Question: Refer back to your prediction? Do you still think that is correct? Change it if you would like. Continue in this manner and record an expression for the volume of a pyramid based on what you just found.

7 At this station, you have a collection of cylinders and cones as well as rice. Using a layer analogy, write an expression for the volume of a cylinder. Question: For a cylinder and cone with congruent bases and congruent heights, how many cones do you think it will take to fill a cylinder? Using the rice/water, fill the cone. Pour this volume into the respective cylinder. Question: Refer back to your prediction? Do you still think that is correct? Change it if you would like. Continue in this manner and record an expression for the volume of a cone based on what you just found.

8 At this station, you have a collection of spheres as well as rice. Using the cone and the cylinder, how many cones will fill the cylinder? Using the cone and the sphere, how many cones will fill the sphere? What are the dimensions of the cone, cylinder, and sphere in terms of the radius of the sphere? What is an equation for the volume of the cylinder in terms of the radius of the sphere? How are the volume of the sphere and the volume of the cylinder related? What is an equation for the volume of a sphere?