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yulyashka [42]
2 years ago
12

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)
Mathematics
2 answers:
Andreas93 [3]2 years ago
8 0

9514 1404 393

Answer:

  • 84 small cubes
  • 3 1/9 unit cubes

Step-by-step 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

__

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

__

<em>Additional comment</em>

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.

likoan [24]2 years ago
5 0

Answer:

can you markk me im sorry

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