Cross Sections and Rotating 2D Shapes

Circle

Rectangle

Triangle

Trapezoid

pyramid

sphere

cylinder

cone

Parabola

Ellipse

Circle

Square

I and II

I, II and III

I, II and IV

I, II, III, and IV

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.

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.

Circle

Triangle

Rectangle

Trapezoid

Sphere

Pyramid

Cylinder

Cone

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.

Dome

Circle

Ellipse

Rectangle