Cavalieri's Principle Worksheet
Grade 12 Math worksheet on Cavalieri's Principle, exploring its application to calculate volumes of various solids.
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Cavalieri's Principle
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Read each question carefully and provide detailed answers. Show all your work for calculations.
1. Which of the following statements best describes Cavalieri's Principle?
If two solids have the same height and the same cross-sectional area at every level, then they have the same surface area.
If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.
If two solids have the same base area and the same height, then they have the same volume.
Cavalieri's Principle only applies to prisms and cylinders.
2. A right circular cylinder has a radius of 5 cm and a height of 10 cm. If an oblique circular cylinder has the same radius and height, what can be said about their volumes?
The oblique cylinder has a larger volume.
The right cylinder has a larger volume.
They have the same volume.
Their volumes cannot be compared without more information.
3. Cavalieri's Principle is often used to demonstrate that the volume of an oblique prism is equal to the volume of a prism with the same base area and .
4. The principle states that if two solids lie between two parallel planes, and every plane parallel to these two planes intersects both solids in cross-sections of equal , then the two solids have equal volumes.
5. Explain Cavalieri's Principle in your own words, providing an example of how it can be applied to compare the volumes of two different shapes.
Match the term with its definition or related concept.
6. Cross-sectional area
a. A solid with two parallel and congruent bases connected by lateral faces that are parallelograms.
7. Oblique solid
b. The area of the shape formed when a plane intersects a solid.
8. Prism
c. A solid whose axis is not perpendicular to its base.
9. Consider a stack of 100 identical circular coins. If you arrange them in a perfectly vertical stack, they form a cylinder. If you push the stack so that it leans to one side, it forms an oblique cylinder. Using Cavalieri's Principle, explain why the volume of the two stacks would be the same.