Understanding Cavalieri's Principle (T)
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Concept-Building Question 2
The figures below have the same base area and height. Do we know whether these have the same volume?

Here, students must decide whether the conclusion from the previous slide can be generalized to apply to non-prisms as well as prisms. The complexity of the figure on the right may prompt students to answer "no," as desired. If more guidance is needed, consider asking,

Is finding the volume of the figure on the right as simple as multiplying its base area by its height?

Students should understand that there is not enough information presented about the figure on the right to determine that its volume is simply the product of its base area and height. What they should also understand is that there is something that is true about the cross-sections of two right prisms of the same base area and height that is not true in the case of the figures below. The next four slides are designed to lead students to this latter understanding, prefaced by the statement below.

Right prisms of the same base area and height have an important characteristic that is missing in these two figures, which will be discussed in the next few slides.



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RadEditor - HTML WYSIWYG Editor. MS Word-like content editing experience thanks to a rich set of formatting tools, dropdowns, dialogs, system modules and built-in spell-check.
RadEditor's components - toolbar, content area, modes and modules
   
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Content area wrapper
RadEditor's bottom area: Design, Html and Preview modes, Statistics module and resize handle.
It contains RadEditor's Modes/views (HTML, Design and Preview), Statistics and Resizer
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