Cross Section and Area

Which best describes the cross-section?

• square

• triangle

• parallelogram

• hexagon

Tags

CCSS.7.G.A.3

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.

Determine whether the 3-D figures are congruent to each other. (Hint: Find the area of the cross-sectional shapes).

• False. Although the cross-sectionals' area and heights of the 3-D figures are the same,the shapes are not congruent

• True. The cross-sectionals' area and the heights of the 3-D figures are the same. They don't have to be the same shape.

• False. The cross-sections are not the same shape.

• True. All the shapes are 3-D figures and the same height.

Tags

CCSS.8.G.A.2

Jenny says that the two prisms DO NOT have the same volume because the cross sections are not the same. Renee disagrees; she says that it isn't the shape that has to be the same but the area. Renee thinks they have the same volume.

Who is correct?

• Jenny

• Renee

• Neither Jenny or Renee is correct.

Tags

CCSS.5.MD.C.5C

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.
  

Describe the cross-section.

• square

• rectangle

• triangle

• circle

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

According to Cavalieri's Principle, how many disks can fit inside of the cone?

• 8 disks

• 12 disks

• 20 disks

• 6 disks

Andrew had a piece of foam shaped like a rectangular prism. The cube was 3in long and 5in tall. He cut the foam on the diagonal. Which is the closest to the area of the shaded plane? (hint-2 steps)

• 19.3 square in

• 12 square in

• 15.8 square in

• 17.5 square in

Tags

CCSS.7.G.A.3

A square pyramid is cut along the shaded plane shown below. Which of the following is a cross-section of the solid?

• 
• 
• 
• 

Tags

CCSS.7.G.A.3