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M2-037-A10-V02
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G-GMD.1
Warmup
M2-037-A10-V02
Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.
Use Cavalieri's principle to compare volumes
Problem
Using \(\text{Cavalieri}'s~\text{principle}\), what can you conclude about the volumes of an oblique cylinder and right cylinder with the same base area and height?
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A
By Cavalieri’s principle, the oblique cylinder must have a different volume because the slanted side makes its slices longer than those of the right cylinder.
B
By Cavalieri’s principle, you cannot conclude the volumes are equal from base area and height alone because the cylinders would need the same radius at every level.
C
By Cavalieri’s principle, the oblique cylinder and the right cylinder have the same volume because they have the same base area, the same height, and equal cross-sections at every level.
D
By Cavalieri’s principle, the two cylinders have the same volume only if the oblique cylinder can be rotated to match the right cylinder exactly.
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Curriculum context
Standard G-GMD.1
Category Geometry
Domain Geometric Measurement and Dimension
Objective Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.
Problem type Use Cavalieri's principle to compare volumes
