MATH 6 Q4 W1

1. Claire makes models to show the relationship between the volume of a rectangular prism and the volume of a rectangular pyramid. The rectangular prism model has a base area of 8 square inches and a height of 12 inches. She also makes a rectangular pyramid with a base and height congruent to the corresponding parts of the prism. Which conclusion is INCORRECT about the relationship between the volumes of the models?

• A.
  The volume of the rectangular prism is triple the volume of the

  rectangular pyramid.

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

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

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

2. Dino has a cone-shaped container that he fills with water. He pours the water into the cylindrical shaped container. Both containers have the same height and bases. Which of the following statements is CORRECT after he pours the water from the cone to the cylinder?

• A.
  The cylindrical shaped container is completely filled with water.

• B.
  Only three-fourths of the volume of cylindrical container is filled with water.

• C.
  One-third of the volume of the cylindrical container is not filled with water.

• D.
  Two-thirds of the volume of the cylindrical container is not filled with water.

3. A spherical tank for natural gas has a volume of about 1500 m³. How will you compare its volume to a cylindrical type of tank having the same dimensions?

• A.
  The volume of the spherical tank is two-thirds of the volume of the cylindrical tank.

• B.
  The volume of the spherical tank is greater than the

  volume of the cylindrical tank.

• C.
  The volumes of the spherical and the cylindrical tanks are the same.

• D.
  The volume of the spherical tank is one-third of the volume of the cylindrical tank.

4. The area of the base of a rectangular prism is 15 m² and the height measures 5 m. What is the volume of the pyramid with the same dimensions as the rectangular prism?

• A.
  The volume of pyramid is 25 m³.

• B.
  The volume of pyramid is 35 m³.

• C.
  The volume of pyramid is 45 m³.

• D.
  The volume of pyramid is 55 m³.

5. 5. Oscar fills a cone-shaped container with water. He pours the water into the cylindrical-shaped container. The height and the bases of the containers have the same measurements. Which of the following statements is INCORRECT after he pours the water from the cone to the cylinder?

• A.
  The cylindrical-shaped container is one-third filled with water.

• B.
  The cylindrical shaped container is completely filled with water.

• C.
  The volume of the cone-shaped container filled with water is one-third of

  the volume of the cylindrical-shaped container.

• D.
  The volume of the cylindrical-shaped container filled with water is three

  times the volume of the cone-shaped container.

6. 6. A rectangular prism and a pyramid have congruent bases and equal altitudes. What is the ratio between the volume of the pyramid to the volume of the rectangular prism?

7. The cylinder below has a base and vertical height congruent to that of the cone. Which best describes the volume of the cone?

8. Which of the following describes the relationship of the volume of cylinder and sphere with the same dimensions?

• A.
  The volume of sphere is one-half the volume of cylinder.

• B.
  The volume of sphere is one-third of the volume of cylinder.

• C.
  The volume of sphere is two-thirds of the volume of cylinder.

• D.
  The volume of sphere is the same with the volume of cylinder.

9. Elena has a cylindrical shaped container that is 9 inches high with a diameter of 10 inches. Reggie has a sphere-shaped container that has a radius of 4 inches. About how much more volume does Elena’s container have than Reggie’s?

• A.
  438.55 inches³

• B.
  325.23 inches³

• C.
  342.54 inches³

• D.
  121.56 inches³