Quiz about Cavalieri's Principle: Volume Formulas Argument

Question 1

Which 3D Figures make up the following composite solid.

Accepted Answer

Cylinder

Accepted Answer

Rectangular Prism

Answer

Sphere

Answer

Pyramid

Question 2

Which 3D Figures make up the following composite solid.

Accepted Answer

Cone

Accepted Answer

Cylinder

Answer

Pyramid

Answer

Rectangular Prism

Question 3

Find the volume of the composite space figure.

Accepted Answer

$$V\ =\ 5,760\ +\ 90\pi\ \cong\ 6,042.7\ m^3$$

Answer

$$V\ =5,500\ +\ 90\pi\ \cong5,782.7\ m^3$$

Answer

$$V\ =\ 5,760\ +\ 360\pi\ \cong6,891\ m^3$$

Answer

$$V\ =\ 5,760\ -\ 90\pi\ \cong\ 5,477.2\ m^3$$

Question 4

Find the volume of the composite figure.

Accepted Answer

$$V\ =\ 594\ +\ 114.4\pi\cong\ 953.4\ mm^3$$

Answer

$$V\ =594\ -\ 114.4\pi\ \cong234.6\ mm^3$$

Answer

$$V\ =\ 594\ +\ 445.5\pi\ \cong\ 1,993.6\ mm^3$$

Answer

$$V\ =\ 594\ -\ 445.5\pi\ \cong283\ mm^3$$

Question 5

Find the volume of the composite figure.

Accepted Answer

$$V\ =\ 1,728\ -12\pi\ \cong1,690.3\ mm^3$$

Answer

$$V\ =\ 1,728\ +\ 12\pi\ \cong1,765.7\ mm^3$$

Answer

$$V\ =\ 1,728\ -\ 48\pi\ \cong\ 1,577.2\ mm^3$$

Answer

$$V\ =\ 1,728\ +\ 48\pi\ \cong1,878.8\ mm^3$$

Question 6

Find the volume of the composite figure.

Accepted Answer

$$V\ =\ 216\ -\ 8\pi\ \cong190.9\ cm^3$$

Answer

$$V\ =216\ +\ 8\pi\ \cong241.1\ cm^3$$

Answer

$$V\ =216\ +\ 96\pi\ \cong\ 517.6\ cm^3$$

Answer

$$V\ =\ 144\ -24\pi\ \cong68.6\ cm^3$$

Question 7

What is the volume of the solid shown below?

Accepted Answer

$$255\ in^3$$

Answer

$$225\ in^3$$

Answer

$$285\ in^3$$

Answer

$$360\ in^3$$

Question 8

Find the volume of the roll of duct tape.

Accepted Answer

9.5

Answer

7.2

Answer

15.3

Answer

21.6

Question 9

What is the volume of this composite figure? Use the pi button on your calculator and round the answer to the nearest tenth.

Accepted Answer

1206.4 ft³

Answer

4825.5 ft³

Question 10

Find the Volume

Accepted Answer

72 cubic cm

Answer

24 cubic cm

Answer

576 cubic cm

Answer

48 cubic cm

Question 11

Describe the cross section.

Accepted Answer

triangle

Answer

rectangle

Answer

trapezoid

Answer

square

Question 12

What shape will the vertical cross -section of a cylinder be?

Accepted Answer

Rectangle

Answer

Circle

Answer

Triangle

Answer

Ellipse

Question 13

Describe the cross-section.

Accepted Answer

triangle

Answer

square

Answer

rectangle

Answer

circle

Question 14

Which best describes the cross-section?

Accepted Answer

square

Answer

triangle

Answer

parallelogram

Answer

hexagon

Question 15

According to Cavalieri's Principle, how many disks could fit inside the cylinder?

Accepted Answer

10 disks

Answer

12 disks

Answer

6 disks

Question 16

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

Accepted Answer

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.

Answer

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

Answer

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

Answer

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

Question 17

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?

Accepted Answer

Renee

Answer

Jenny

Answer

Neither Jenny or Renee is correct.

Question 18

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

Accepted Answer

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

Answer

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

Question 19

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

Accepted Answer

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

Answer

True

Answer

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

Answer

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

Question 20

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

Accepted Answer

These WILL have the same volume

Answer

These COULD have the same volume

Answer

These WILL NOT have the same volume

Answer

Not enough information

Question 21

How do the figures volumes' compare?

Accepted Answer

They are equal.

Answer

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

Answer

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

Answer

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

Cavalieri's Principle: Volume Formulas Argument

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