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

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

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

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

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?

Neither Jenny or Renee is correct.

Based on Cavalieri's Principle, will the two prisms have the same volume?

Yes, the heights of both prisms are the same and they have the same cross-sectional area. Therefore, they will have the same volume.

No, they will not be same. Although the heights are the same, the cross-sections are different shapes.

a) Cavalieri’s Principle states that any two objects with equal volume must have the same height.

False - if two objects have the same base and height, they must have the same volume.

False - if two objects have equal volume must have the same BASE, not height

False - if two objects have equal volume must have the same SLANT HEIGHT, not height

An oblique shape will always have the same volume as a right shape if they have the same base.

False - an oblique shape will always have the same volume as a right shape if they have the same base AND height

False - an oblique shape and a right shape can never have the same volume

False - an oblique shape and a right shape can't have the same base

a) A cone and a pyramid with equal base areas and heights

These WILL have the same volume

These COULD have the same volume

These WILL NOT have the same volume

How do the figures volumes' compare?

The right prism has a larger volume than the oblique prism.

The oblique prism has a larger volume than the right prism.

The right prism has a volume that is twice as large as the oblique prism.

Cavalieri's Principle: Volume Formulas Argument

Authored by Barbara White

Mathematics

9th - 10th Grade

CCSS covered

Cavalieri's Principle: Volume Formulas Argument

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MULTIPLE SELECT QUESTION

1 min • 1 pt

Which 3D Figures make up the following composite solid.

Sphere

Cylinder

Pyramid

Rectangular Prism

Tags

CCSS.1.G.A.2

MULTIPLE SELECT QUESTION

1 min • 1 pt

Which 3D Figures make up the following composite solid.

Cone

Cylinder

Pyramid

Rectangular Prism

Tags

CCSS.1.G.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the volume of the composite space figure.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the volume of the composite figure.

Tags

CCSS.5.MD.C.5C

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the volume of the composite figure.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the volume of the composite figure.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which equation would you use to find the volume of this composite figure?

8³ + ⁴/₃π(8)³

8³ + ⁴/₃π(4)³

8³ + (¹/₂)(⁴/₃)π(4)³

Tags

CCSS.5.MD.C.5C

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Cavalieri's Principle: Volume Formulas Argument

Which 3D Figures make up the following composite solid.

Which 3D Figures make up the following composite solid.

Find the volume of the composite space figure.

Find the volume of the composite figure.

Find the volume of the composite figure.

Find the volume of the composite figure.

Which equation would you use to find the volume of this composite figure?

Which equation would you use to find the volume of this composite figure?

What is the volume of the solid shown below?

What is the volume of this figure?

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