Makeup work_ Cavalieri's principle

Makeup work(

Multiple Choice

• Only A & B

• Only A & C

• Only B & C

• A, B and C

Multiple Choice

• The base areas are not the same.

• It isn’t true that corresponding cross-sections have the same area.

• The heights are not the same.

Multiple Choice

• The base areas are not the same.

• It isn’t true that corresponding cross-sections have the same area.

• She did not establish that heights are the same.

Multiple Choice

• The base areas are not the same.

• It isn’t true that corresponding cross-sections have the same area.

• The heights are not the same.

Multiple Choice

Right triangle ABC has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around AB ?

• 32π

• 48π

• 96π

• 144π

Multiple Choice

Triangle ABC, with vertices at A(0,0), B(3,5), C(0,5) and , is graphed. Which figure is formed when ΔABC is rotated continuously about BC?

Multiple Choice

What solid 3D object is produced by rotating the triangle around line m?

• Triangular Prism

• Cylinder

• Cone

• Triangular Pyramid

Multiple Choice

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

Multiple Choice

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.

Multiple Choice

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.

Multiple Choice

Based on Cavalieri's Principle, will the two prisms have the same volume? (Remember to look at the height.)

• 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.
  

Multiple Choice

According to Cavalieri's Principle, how many disks could fit inside the cylinder? (Remember to look at the height.)

• 12 disks

• 6 disks

• 10 disks

Multiple Choice

a) 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.

Multiple Choice

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.

Multiple Choice

Identify the cross section formed in the picture.

• square
• rectangle
• parallelogram
• pentagon

Multiple Choice

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

• Dome
• Circle
• Ellipse
• Rectangle

Multiple Choice

Describe the cross section.

• trapezoid
• triangle
• rectangle
• square

Multiple Choice

Describe the cross section.

• rectangle
• trapezoid
• oval
• parallelogram

Multiple Choice

Describe the cross section.

• circle

• oval

• semi-circle

• trapezoid

Multiple Choice

Describe the cross section.

• circle
• oval
• semi-circle
• trapezoid