CAVALIERI'S PRINCIPLE

Multiple Choice

a) Cavalieri’s Principle states that any two objects with equal volume must have the same height.

• True

• False - if two objects have equal volume must have the same BASE, not height

• False - if two objects have equal volume must have the same SLANT HEIGHT, not height

• False - if two objects have the same base and height, they must have the same volume.

Multiple Choice

An oblique shape will always have the same volume as a right shape if they have the same base.

• True

• False - an oblique shape and a right shape can never have the same volume

• False - an oblique shape and a right shape can't have the same base

• False - an oblique shape will always have the same volume as a right shape if they have the same base AND height

Multiple Choice

a) Cavalieri’s Principle states that any two objects with the same cross sectional areas and heights must have the same volume.

• True

• False - the cross sectional areas are not relevant

• False - only the slant height is relevant

• False - even if they have the same cross sectional areas and heights, they cannot have the same volume.

Multiple Choice

a) A cone and a pyramid with equal base areas and heights

• These COULD have the same volume

• These MUST have the same volume

• These MUST NOT have the same volume

• Not enough information

Multiple Choice

b) A cylinder and a right rectangular prism with equal heights

• These COULD have the same volume

• These MUST have the same volume

• These MUST NOT have the same volume

• Not enough information

Multiple Choice

c) A cylinder and a cone with the same radius

• These COULD have the same volume

• These MUST have the same volume

• These MUST NOT have the same volume

• Not enough information

Multiple Choice

d) A cone and a cylinder with equal base areas and heights

• These COULD have the same volume

• These MUST have the same volume

• These MUST NOT have the same volume

• Not enough information

Multiple Choice

e) A prism and a cylinder with equal base areas and heights

• These COULD have the same volume

• These MUST have the same volume

• These MUST NOT have the same volume

• Not enough information

Multiple Select

Explain what this image is trying to show

• How to calculate the area of the triangles

• That the two triangles have the same area

• That parallel lines show the angles are congruent, therefore the triangles are congruent by ASA

• How to apply the pythagorean theorem

Multiple Choice

The shapes below have the Base Areas and Heights. Which will have the same volume. Which ones will have the same volumes based on Cavalieri's Principle?

• Rectangular Pyramid and Triangular Prism

• Rectangular Pyramid and Cylinder

• Triangular Prism and Cylinder

• All three.

Multiple Choice

The shapes below have the Base Areas and Heights. Which will have the same volume. Which ones will have the same volumes based on Cavalieri's Principle?

• Rectangular Pyramid and Triangular Prism

• Rectangular Pyramid and Cone

• Triangular Prism and Cone

• All three.

Multiple Choice

Based on Cavalieri's Principle, will the two prisms have the same volume?

• No, they will not be same. Although the heights are the same, the cross-sections are different shapes. 

• Yes, the heights of both prisms are the same and they have the same cross-sectional area. Therefore, they will have the same volume.