Cavalieri's Principle, Cross Sections

Describe the cross section.

• triangle
• rectangle
• trapezoid
• square

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

• Dome
• Circle
• Ellipse
• Rectangle

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

• Circle
• Triangle
• Rectangle
• Ellipse

Describe the cross-section.

• square
• rectangle
• triangle
• circle

Which best describes the cross-section?

• square
• triangle
• parallelogram
• hexagon

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

• 12 disks

• 6 disks

• 10 disks

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.

Determine whether the 3-D figures are congruent to each other. (Hint: Find the area of the cross-sectional shapes).

• False. Although the cross-sectionals' area and heights of the 3-D figures are the same,the shapes are not congruent

• True. The cross-sectionals' area and the heights of the 3-D figures are the same. They don't have to be the same shape.

• False. The cross-sections are not the same shape.

• True. All the shapes are 3-D figures and the same height.

Jenny says that the two prisms DO NOT have the same volume because the cross sections are not the same. Renee disagrees; she says that it isn't the shape that has to be the same but the area. Renee thinks they have the same volume.

Who is correct?

• Jenny

• Renee

• Neither Jenny or Renee is correct.

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.