Cavalieri's Principle Worksheet
Explore Cavalieri's Principle with this Grade 11 math worksheet, featuring questions on comparing volumes of solids with equal heights and cross-sectional areas.
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Cavalieri's Principle Worksheet
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Read each question carefully and answer to the best of your ability. Show all work where applicable.
1. State Cavalieri's Principle in your own words, for both two-dimensional and three-dimensional figures.
2. Two solids have the same height. If every cross-section parallel to their bases has the same area, what can be concluded about their volumes?
Their volumes are always different.
Their volumes are always equal.
Their volumes are sometimes equal, sometimes different.
There is not enough information to conclude.
3. A stack of pennies that is perfectly vertical has the same volume as a stack of pennies that is leaning, provided both stacks have the same number of pennies and the same .
4. Consider a right circular cylinder and an oblique circular cylinder with the same base radius and height. According to Cavalieri's Principle, their volumes are equal.
True
False
5. A stack of 100 identical circular poker chips forms a cylinder with a height of 5 cm. If the stack is pushed so that it forms an oblique cylinder, but the base area and the total height remain the same, what can you say about the volume of the new stack compared to the original stack? Explain your reasoning.
Match each solid figure description on the left with the correct statement regarding Cavalieri's Principle on the right.
1. A right rectangular prism
a. Can be compared to an oblique prism with equal volume.
2. Two cones with different base shapes but equal base areas and heights
b. Cannot be directly compared using Cavalieri's Principle.
3. A sphere and a cylinder that have the same height and equal cross-sectional areas at every level
c. Their volumes are equal by Cavalieri's Principle.