Question

The dimensions of a rectangular prism are shown below:

Length: 5 feet
Width: 1 foot
Height: 27/3 feet

The lengths of the sides of a small cube are 3 feet each.

Part A: How many small cubes can be packed in the rectangular prism? Show your work.
Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube.

Answer 1

Part A: 1 small cube can be packed in the rectangular prism. Part B: The volume of the rectangular prism is 27 cubic feet.

Step-by-step explanation:

Part A: To find out how many small cubes can be packed in the rectangular prism, we need to determine the volume of the rectangular prism and the volume of a small cube. The volume of the rectangular prism is calculated by multiplying its length, width, and height. In this case, the volume of the rectangular prism is 5 feet x 1 foot x (27/3) feet = 45 cubic feet. The volume of a small cube is calculated by raising the length of its side to the power of 3. Since each side of the small cube is 3 feet long, the volume of the small cube is 3 feet x 3 feet x 3 feet = 27 cubic feet.

To determine how many small cubes can be packed in the rectangular prism, we divide the volume of the rectangular prism by the volume of a small cube. In this case, 45 cubic feet ÷ 27 cubic feet = 1.67. Since we cannot have a fraction of a cube, we round down to the nearest whole number. Therefore, we can pack 1 small cube inside the rectangular prism.

Part B: Since we determined that the rectangular prism can hold 1 small cube, the volume of the rectangular prism in terms of the small cube and a unit cube is simply the volume of a small cube, which is 27 cubic feet.