Use the image to answer the question.

An illustration shows a rectangular prism made of cubes placed as 3 columns, 2 cubes high and 2 cubes deep.

Find the volume of the right rectangular prism packed with 12 cubes. Each cube has an edge length of 12
inch.

(1 point)
Responses

5 cubic inches
5 cubic inches

12 cubic inches
12 cubic inches

18
cubic inches
Start Fraction 1 over 8 End Fraction cubic inches

32
cubic inches
Start Fraction 3 over 2 End Fraction cubic inches
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1 answer

To calculate the volume of the rectangular prism made of cubes, we first need to determine the volume of one individual cube and then multiply by the total number of cubes.

  1. Volume of One Cube: The formula for the volume of a cube is:

    \[ \text{Volume} = \text{edge length}^3 \]

    Given that the edge length of each cube is 12 inches:

    \[ \text{Volume of one cube} = 12 , \text{inches} \times 12 , \text{inches} \times 12 , \text{inches} = 12^3 = 1728 , \text{cubic inches} \]

  2. Total Volume of the Rectangular Prism: Since there are 12 cubes in total, the total volume of the right rectangular prism packed with those cubes is:

    \[ \text{Total Volume} = 12 \times 1728 , \text{cubic inches} = 20736 , \text{cubic inches} \]

None of the provided responses matches this calculated total volume, indicating there may have been a misunderstanding regarding the options or the context of the question. However, the volume of the rectangular prism containing 12 cubes of 12-inch edge length each is 20736 cubic inches.