Question

The dimensions of a rectangular prism are shown below: Length: 1 and 1 over 3 feet Width: 1 foot Height: 2 and 1 over 3feet The lengths of the sides of a small cube are 1 over 3 foot each. Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points) 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. (5 points)

Answer 1

A:84 B:?

Explanation:

Answer 2

9514 1404 393

Answer:

• 84 small cubes
• 3 1/9 unit cubes

Explanation:

A cube that is 1/3 ft on a side will fit 3 in a foot. In terms of the 1/3 ft small cube, the dimensions of the prism are ...

1 1/3 ft = 4 small cubes

1 ft = 3 small cubes

2 1/3 ft = 7 small cubes

Then the volume in terms of small cubes is ...

V = LWH = (4)(3)(7) = 84 small cubes

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There are 3×3×3 = 27 small cubes in a 1-ft unit cube, so the prism volume in terms of unit cubes is ...

84/27 = 3 1/9 . . . unit cubes

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Additional comment

The largest dimension of the prism is just over 2 ft, so the maximum number of unit (1 ft) cubes that will fit is 2. To fill the volume with 3 1/9 unit cubes, those would have to be cut and fit into the space.