A prism is completely filled with 2304 cubes that have edge length of 1/4 cm

What is the volume of the prism?

2304 * (1/4)^3 = 36 cm^3

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A prism is completely filled with 2304 cubes that have edge length of 14 cm

What is the volume of the prism?

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cm³

36

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To find the volume of the prism, we need to multiply its base area by its height.

The base area can be determined by finding the number of cubes that fit on the base and multiplying it by the area of each cube.

The number of cubes that fit on the base can be found by dividing the total number of cubes (2304) by the number of rows or layers in the prism.

Since each cube has an edge length of 1/4 cm, the area of each cube can be calculated by multiplying the edge length by itself (1/4 cm * 1/4 cm = 1/16 cm^2).

First, let's calculate the number of rows or layers in the prism. Since all the cubes are completely filled inside the prism, we can find the number of rows by finding the square root of the total number of cubes.

√2304 ≈ 48

Therefore, the prism has 48 rows or layers.

Next, let's calculate the base area:

Base Area = Number of cubes in base * Area of each cube

Number of cubes in base = Total number of cubes / Number of rows
Number of cubes in base = 2304 / 48 = 48

Area of each cube = (1/4 cm) * (1/4 cm) = 1/16 cm^2

Base Area = 48 * 1/16 cm^2 = 48/16 cm^2 = 3 cm^2

Finally, let's calculate the volume of the prism:

Volume = Base Area * Height

Since the prism is completely filled with cubes, the height of the prism is equal to the length of each cube, which is 1/4 cm.

Volume = (3 cm^2) * (1/4 cm) = 3/4 cm^3

Therefore, the volume of the prism is 3/4 cm^3.