Geometry
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Volume
Posted on May 6, 2010
Topic: 3-Dimensional Geometry
Students define right and oblique three dimensional figures and calculate the volume for prisms, pyramids, cylinders, and cones.
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Activity Key Steps:
Students begin by exploring rectangular prisms. They use an interactive figure built into this activity, seen to the right. They drag the vertices of the prism and explore various shapes it takes on. Students must pay close attention to which vertex affects the length, width, and height of the prism.
Problem 2 gives students the opportunity to explore triangular prisms and pyramids. Students use the given triangular prism to find its volume. They use the Calculate command and select the values needed to solve the area of a triangle B = ½• b • h; and the volume V = B • h.
In this problem, students will also discuss the difference between prisms and pyramids.
Students move on to Problem 3 where they investigate the volume of a right cylinder and a cone. As before, students can drag the open points to change the height and radius of the base.
The final figure that students encounter is a cone. They will calculate the volume of the cone. Students should observe that if a cone and a cylinder have the same radius and same height, the volume of the cone is one-third the volume of a cylinder.
At the end of this activity, students will be able to find the volume of a cylinder, cone, prism, and pyramid.