Calculus Volume of Solid Known Cross Section

Which 3-D solid is created when the rectangle is rotated about the horizontal line?

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What 3-D solid is formed when this rectangle is rotated about the vertical line?

• Right, rectangular prism

• Right, circular cylinder

• Right, oval cylinder

• Right, square prism

Describe the cross section.

• triangle

• rectangle

• oval

• trapezoid

Describe the cross section.

• rectangle

• trapezoid

• parallelogram

• triangle

• cone

• cylinder

• pyramid

• prism

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.
  

Which 2-D shape could be revolved about the vertical line to create the 3-D solid?

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