Two stacks of 23 quarters each are shown. One stack forms a cylinder but the other stack does not form a cylinder. Stack 1 Stack 2 Why are the volumes of these two stacks of quarters equal? Use Cavalieri's Principle to explain your thinking.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Every cross section parallel to the bases has an equal area. Because the stacks
are the same height, the stacks must have the same volume.
If Stack 1 was twisted it would look like Stack 2, so the stacks must have the
same volume.
Every cross section perpendicular to the bases has an equal area. Because both
stacks have height, the stacks must have the same volume.
If Stack 2 was straightened it would look like Stack 1, so the stacks must have
the same volume.
Transcribed Image Text:Every cross section parallel to the bases has an equal area. Because the stacks are the same height, the stacks must have the same volume. If Stack 1 was twisted it would look like Stack 2, so the stacks must have the same volume. Every cross section perpendicular to the bases has an equal area. Because both stacks have height, the stacks must have the same volume. If Stack 2 was straightened it would look like Stack 1, so the stacks must have the same volume.
Two stacks of 23 quarters each are shown. One stack forms a cylinder but the other
stack does not form a cylinder.
Stack 1
Stack 2
Why are the volumes of these two stacks of quarters equal? Use Cavalieri's Principle
to explain your thinking.
Transcribed Image Text:Two stacks of 23 quarters each are shown. One stack forms a cylinder but the other stack does not form a cylinder. Stack 1 Stack 2 Why are the volumes of these two stacks of quarters equal? Use Cavalieri's Principle to explain your thinking.
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