Question

If a right rectangular prism is packed with 12 cubes, each cube being the length of 1/2 inch, with 2 cubes height, 3 cubes in length and 2 cubes in width, what’s the volume

Answer 1

To find the volume of the right rectangular prism that is packed with the cubes, we first determine the dimensions of the prism based on the cubes.

Each cube has a side length of \( \frac{1}{2} \) inch.

The dimensions of the prism in terms of cubes are:
- Height: 2 cubes
- Length: 3 cubes
- Width: 2 cubes

Now we convert these dimensions from cubes to inches:
- Height in inches: \( 2 \text{ cubes} \times \frac{1}{2} \text{ inch/cube} = 1 \text{ inch} \)
- Length in inches: \( 3 \text{ cubes} \times \frac{1}{2} \text{ inch/cube} = 1.5 \text{ inches} \)
- Width in inches: \( 2 \text{ cubes} \times \frac{1}{2} \text{ inch/cube} = 1 \text{ inch} \)

Now, we can calculate the volume of the right rectangular prism using the formula for the volume of a rectangular prism, which is:
\[
\text{Volume} = \text{Height} \times \text{Length} \times \text{Width}
\]

Substituting the dimensions:
\[
\text{Volume} = 1 \text{ inch} \times 1.5 \text{ inches} \times 1 \text{ inch}
\]
\[
\text{Volume} = 1 \times 1.5 \times 1 = 1.5 \text{ cubic inches}
\]

Thus, the volume of the right rectangular prism is \( \boxed{1.5} \) cubic inches.