Cross Sections and Volume of Right Prisms

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.
  

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

• 150.8

• 1504.1

• 1529.2

• 1680

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.

Find the volume.

• 1,444.48 ft³

• 1,745.92 ft³

• 2,132.08 ft³

• 2,951.68 ft³

Describe the cross section.

• triangle

• rectangle

• oval

• trapezoid

What is the area of the cross-section if the diameter of the base is 6 feet and the height of the cylinder is 8 feet.

• 24 ft²

• 48 ft²

• 8 ft²

• 4 ft²

Which figure describes the two-dimensional cross section?

• triangle

• rectangle

• pentagon

• hexagon

What is the volume of this rectangular prism?

• 60 cubic centimeters

• 15 cubic centimeters

• 20 cubic centimeters

• 6 cubic centimeters

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.

Sheila believes that the two cylinders shown in the diagram below have equal volumes. Is Sheila correct or incorrect? Select ALL that apply.

• Sheila is incorrect. The volumes of both cylinders are not equal.

• Sheila is incorrect. One of the cylinders is tilted.

• Sheila is correct. When two cylinders have the same base areas and the same height, their volumes must be the same.

• Sheila is correct. Both cylinders radii and height are equal, so their volumes are the same.

•  

  Sheila is correct. Using Cavalieri’s Principle and the formula v=Bh or  V=πr2h  proves the volumes of the cylinders are equal.