Cavalieri's Principle

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.

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.2

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

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.2

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.2

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

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.2

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.2

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

According to Cavalieri’s Principle, which of these shapes has a greater area?

• The one on the left

• The one on the right

• They have the same area

• Not enough information

Tags

CCSS.HSG.GMD.A.1

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

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.4

CCSS.HSG.SRT.B.5

CCSS.HSG.SRT.D.9