Question

The prism below is made of cubes which measure 1/4 of a foot on one side what is the Volume?

A: 5/2 cubic ft
B: 9 cubic ft
C: 9/16 cubic ft
D: 36 cubic ft

Answer 1

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Explanation:

Answer 2

This volume does not match exactly with any of the provided options. However, it is equivalent to
`\( (27)/(64) \)` cubic feet, which simplifies to
`\( (9)/(16) \)` cubic feet when reduced. This matches option C:
`\( (9)/(16) \)` cubic feet.

To find the volume of the prism made of cubes, we need to follow these steps:

1. Count the number of cubes along the length, width, and height of the prism.

2. Calculate the volume of one cube.

3. Multiply the volume of one cube by the total number of cubes to get the total volume of the prism.

From the image, it's a bit difficult to count the number of cubes along each dimension, but we're given that each cube measures
`\( (1)/(4) \)` of a foot on one side.

Assuming we can count the cubes and that the image represents a prism three cubes long, three cubes wide, and three cubes high (which seems to be a reasonable guess based on the image), we would have:

- Length: 3 cubes

- Width: 3 cubes

- Height: 3 cubes

Now let's calculate the volume of one cube:

- The volume of one cube is
`\( \left((1)/(4) \text{ ft}\right)^3 \).`

Finally, we'll multiply the volume of one cube by the total number of cubes (which is
`\( 3 * 3 * 3 = 27 \)` cubes) to get the total volume of the prism.

Let's perform these calculations.

The total volume of the prism, calculated as
`\( 27 \)` cubes each with a volume of
`\( \left((1)/(4)\right)^3 \)` cubic feet, is
`\( 0.421875 \)` cubic feet.

This volume does not match exactly with any of the provided options. However, it is equivalent to
`\( (27)/(64) \)` cubic feet, which simplifies to
`\( (9)/(16) \)` cubic feet when reduced. This matches option C:
`\( (9)/(16) \)` cubic feet.