PRACTICE ASSIGNMENT: Cavalieri's Principal

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.

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.
  

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

• 12 disks

• 6 disks

• 10 disks

Two solids have the same height. At every level, the cross-sectional area of the first solid is equal to the cross-sectional area of the second solid. According to Cavalieri's Principle, which of the following statements is true?

• The two solids have different volumes.

• The two solids have the same volume.

• The first solid has a larger volume than the second solid.

• The second solid has a larger volume than the first solid.

Using Cavalieri's Principle, how can you determine if two cylinders have the same volume?

• Compare their heights.

• Compare their base radii.

• Ensure they have the same height and base area.

• Measure the water displacement when submerged.

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.

• The base areas are not the same.

• It isn’t true that corresponding cross-sections have the same area.

• The heights are not the same.

• She never established the heights are the same in her reasoning.

• She never established the bases have the same area in her reasoning.

• She never established the two shapes have the same cross-sectional areas.