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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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.

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.

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

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?

• $\frac{1}{3}\times120\ \times h$

• $\frac{1}{3\ }\times120$

• $3\times120$

• $3\times120\times h$

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.

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.

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?

• $V=15\left(3\right)$

• $V=50\left(3\right)$

• $V=50\left(\frac{1}{3}\right)$

• $V=15\left(\frac{1}{3}\right)$

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.

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