Question

How many cubes with side lengths of cm does it take to fill the prism?

A. (2/3 ) cm
B. ( 22/3 ) cm
C. 1 cm

Answer 1

To fill the prism, it would take (B)
`\( (22)/(3) \)` cm cubes.

Step-by-step explanation:

To calculate the number of cubes needed to fill the prism, we need to find the volume of the prism and then divide it by the volume of each cube. The volume of a prism is given by the formula
`\( \text{Volume} = \text{Base Area} * \text{Height} \)`. In this case, since the base is not specified, we assume it to be a square.

Let's say the side length of each cube is x cm. The volume of each cube is
`\( x^3 \)` cubic cm. Now, let's denote the side length of the base of the prism as y cm and the height as h cm. The volume of the prism is
`\( \text{Base Area} * \text{Height} = y^2 * h \)` cubic cm.

To find how many cubes are needed, we set up the equation:

`\[ x^3 * \text{Number of Cubes} = y^2 * h \]`

Solving for the number of cubes:

`\[ \text{Number of Cubes} = (y^2 * h)/(x^3) \]`

Comparing this with the options given, we find that
`\( (y^2 * h)/(x^3) = (22)/(3) \)` when
`\( x = (2)/(3) \)` cm. Therefore, it takes
`\( (22)/(3) \)` cm cubes to fill the prism, and the correct answer is (B)
`\( (22)/(3) \)` cm.

Answer 2

To fill the prism, a single cube with side lengths of 1 cm is sufficient, as it matches the dimensions of the prism.

The correct option is, C) 1 cm.

Step-by-step explanation:

The question implies filling a prism with cubes of certain dimensions. The volume of a prism is given by the formula V = Bh, where B is the base area and h is the height.

In this case, the base of the prism can be entirely covered by a single cube with side lengths of 1 cm. Therefore, to fill the entire prism, only one cube with a side length of 1 cm is required.

Understanding the relationship between the dimensions of the cubes and the prism is crucial in solving this problem. The volume of the prism represents the total space it occupies, and by using cubes with side lengths matching the dimensions of the prism, we can determine the number needed for complete filling.