Prisms vs Pyramids

Trevor and Matt each build a three dimensional figure as shown. Who built a pyramid?

• Trevor

• Matt

• Neither

• Both

Which statement correctly describes the volume of the two figures?

• The volume of the pyramid is 1/3 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 1/3 greater than the volume of the prism.

Tags

CCSS.5.MD.C.5C

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

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

Tags

CCSS.HSG.GMD.A.3

Which does NOT describe the relationship between the two figures?

• (pyramid volume)(1/3)= prism volume

• (pyramid volume)(3)= prism volume

• (prism volume)(1/3) = pyramid volume

• (prism volume)/3 = pyramid volume

Tags

CCSS.HSG.GMD.A.3

Mallory constructs models to shown the relationship between the volume of a triangular prism and the volume of a triangular pyramid. The triangular prism model has a base area of 6 square inches and a height of 6 inches. Mallory also constructs a triangular pyramid with a base and height congruent to the the corresponding parts of the prism. Which conclusion is NOT true about the relationship between the volumes of the models?

• The volume of the prism is triple the volume of the pyramid.

• The volume of the pyramid is three times the volume of the prism.

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

• The volume of the prism is three times the volume of the pyramid.

Tags

CCSS.HSG.GMD.A.3

Juan has a triangular pyramid-shaped container that he fills with water. He pours the water into a second container that is the shape of a triangular prism. Both containers have congruent heights and bases. After Juan pours the water from the pyramid into the prism, which statement is true?

• Three-fourths of the volume of the prism does not contain water.

• Two-thirds of the volume of the prism does not contain water.

• One-third of the volume of the prism does not contain water

• The triangular prism is completely filled with water.

Tags

CCSS.3.MD.A.2

The base area of a triangular prism is 20 square units. The height of the prism is 12 units. Which of the following best describes the volume of a triangular pyramid with the same dimensions.

• V = 240 units³ because 20(12)= 240

• V = 120 units³ because (1/2)(20)(12) = 120

• V = 720 units³ because (3)(20)(12) = 720

• V = 80 units³ because (1/3)(20)(12) = 80

Tags

CCSS.HSG.GMD.A.3

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

• V = 15(3)

• V = 50(3)

• V = 50(1/3)

• V = 15(1/3)

Tags

CCSS.HSG.GMD.A.3