Cavalieri's Principle and Cross Sections

Describe the cross section.

• triangle
• rectangle
• trapezoid
• square

Tags

CCSS.7.G.A.3

What shape will the horizontal cross-section of a sphere be?

• Dome
• Circle
• Ellipse
• Rectangle

Tags

CCSS.7.G.A.3

What shape will the vertical cross -section of a cylinder be?

• Circle
• Triangle
• Rectangle
• Ellipse

Tags

CCSS.7.G.A.3

Describe the cross-section.

• square
• rectangle
• triangle
• circle

Tags

CCSS.7.G.A.3

Which best describes the cross-section?

• square
• triangle
• parallelogram
• hexagon

Tags

CCSS.7.G.A.3

According to Cavalieri's Principle, how many disks could fit inside the cylinder?

• 12 disks

• 6 disks

• 10 disks

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

According to Cavalieri's Principle, how many disks can fit inside of the cone?

• 8 disks

• 12 disks

• 20 disks

• 6 disks

Tags

CCSS.3.MD.A.2

Sue believes that the two cylinders shown in the diagram below have equal volumes.

• She is not correct because one is slanted.

• She is not correct because one has a radius of 5m and one has a diameter of 10m.

• She is correct because they have the same height of 11.5 m.

• She is correct because one has a height of 11.5m and the other has a height close at 12m.

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Two stacks of 23 quarters each are shown below. One stack forms a cylinder but the other stack does not form a cylinder. However, they have the same volume according to Cavalieri's Principle.

• True

• False

Tags

CCSS.5.MD.C.5C