Cavalieri's Principle: Volume Formulas Argument

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.

What is the exact volume of the pyramid?

• 48 cm³

• 144 cm³

• 288 cm³

• 96 cm³

Tags

CCSS.HSG.GMD.A.3

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.
  

Tags

CCSS.7.G.B.6

Find the volume.

• 1,444.48 ft³

• 1,745.92 ft³

• 2,132.08 ft³

• 2,951.68 ft³

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

• Only A and B

• Only B and C

• Only A and C

• A, B, and C

What is the formula for calculating the volume of a solid using Cavalieri's principle?

• Divide the surface area of the solid by its height.

• Integrate the cross-sectional area of the solid with respect to the height.

• Multiply the base area of the solid by its height.

• Find the average of the base area and the surface area of the solid.

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

• 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.

Determine the volume of the composite solid. Round your answer to the nearest tenth.

• 150.8

• 1504.1

• 1529.2

• 1680

Tags

CCSS.5.MD.C.5C

Describe the cross section.

• circle

• oval

• semi-circle

• trapezoid

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.7.G.B.6