Volume of a Rectangular Prism vs Pyramid 7.8A & B

Which of the following has a volume that is one-third the volume of the figure shown?

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Tags

CCSS.HSG.GMD.A.3

Which statement correctly describes the relationship between a rectangular pyramid and a rectangular prism?

• If the prism and the pyramid have congruent bases, then the volume of the prism is one-third the volume of the pyramid.

• If the pyramid and the prism have congruent bases and equal heights, then the volume of the pyramid is three times the volume of the prism.

• If the prism and the pyramid have congruent bases and equal heights, then the volume of the prism is three times the volume of the pyramid.

• If the pyramid and the prism have congruent bases, then the volume of the pyramid is one-third the volume of the prism.

Tags

CCSS.HSG.GMD.A.3

Which of the following statements about figures A and B is NOT true?

• The volume of figure B is one-third the volume of figure A.

• The volume of figure A can be found by tripling the volume of figure B.

• The volume of figure B can be found by dividing the volume of figure A by three.

• The volume of figure A is one-third the volume of figure B.

Tags

CCSS.3.MD.A.2

Hypnotic Emporium has two different containers customers can choose when they order their ice cream. Rylee chooses the container shown. The second container is a rectangular prism and holds three times as much ice cream and the container Rylee chose. Which of the following best represents the dimensions of the prism-shaped container?

• 4 inches by 4 inches by 4.7 inches

• 12 inches by 9 inches by 12 inches

• 4 inches by 3 inches by 4.7 inches

• 4 inches by 3 inches by 4 inches

Tags

CCSS.7.G.B.6

A rectangular prism has a base that is congruent to the base of a rectangular pyramid. The heights, h, of the two figures are also congruent. If the volume of the pyramid is 120 in³, which expression can be used to find the volume of the prism?

• $\frac{1}{3}\times120\ \times h$

• $\frac{1}{3\ }\times120$

• $3\times120$

• $3\times120\times h$

Tags

CCSS.HSG.GMD.A.3

Which statement correctly describes the volumes of the two figures?

• The volume of the pyramid is one-third the volume of the prism.

• The volumes are the same because the base areas are the same.

• The volumes are the same because the dimensions are the same.

• The volume of the pyramid is one-third greater than the volume of the prism.

Tags

CCSS.HSG.GMD.A.3

The heights and areas of the bases of a rectangular pyramid and a rectangular prism are congruent. Brooklyn calculates the volume of the prism to be 6 cubic units and the volume of the pyramid to be 3 cubic units. Which statement about Brooklyn's calculations is true?

• Brooklyn is incorrect because the pyramid's volume is not 3 times the prism's volume.

• Brooklyn is incorrect because the prism's volume is not 3 times the pyramid's volume.

• Brooklyn is correct becuase the pyramid's volme is one-third the prism's volume.

• Brooklyn is correct because the prism's volume is four-thirds the pyramid's volume.

Tags

CCSS.HSG.GMD.A.3

If a rectangular pyramid has a base and a vertical height congruent to that of the rectangular prism, which best describes the volume of the pyramid?

• $V=15\left(3\right)$

• $V=50\left(3\right)$

• $V=50\left(\frac{1}{3}\right)$

• $V=15\left(\frac{1}{3}\right)$

Tags

CCSS.HSG.GMD.A.3

Jaylen and Savannah make 3-D figures out of clay. Jaylen makes a rectangular pyramid like the one shown, using 32 cubic inches of clay. If Savannah makes a rectangular prism with the same dimensions as Jaylen's pyramid, she will use ____ cubic inches of clay.

Tags

CCSS.HSG.GMD.A.3

Write a statement generalizing the relationship between the volume of a rectangular pyramid and the volume of a rectangular prism.

Tags

CCSS.HSG.GMD.A.3