Cross Sections and Rotating 2D Shapes

A cylinder is cut parallel to the base. What is the shape of the cross-section formed?

• Circle

• Rectangle

• Triangle

• Trapezoid

Rotating this circle around the diameter creates a ____________.

• pyramid

• sphere

• cylinder

• cone

Which shape is NOT a cross section of a cone?

• Parabola

• Ellipse

• Circle

• Square

Which of the shapes are possible cross-sections of a cube?

• I and II

• I, II and III

• I, II and IV

• I, II, III, and IV

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.
  

A cone is cut by a plane that is perpendicular to its base. Which of the following could be the shape of the cross-section formed?

• Circle

• Triangle

• Rectangle

• Trapezoid

The cross-section of a 3D figure is shaped like a circle. Which could NOT have been the 3D figure?

• Sphere

• Pyramid

• Cylinder

• Cone

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.

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

• Dome

• Circle

• Ellipse

• Rectangle