Find the volume of the right rectangular prism packed with 12 cubes. Each cube has an edge length of 1/2 inch.

(1 point)
Responses

1/8 cubic inches

12 cubic inches

5 cubic inches

3/2 cubic inches
Given:
a cube with 12 small cubes

1 answer

To find the volume of the right rectangular prism packed with 12 cubes, we first need to calculate the volume of a single cube and then multiply it by the total number of cubes.

  1. Volume of a single cube: The formula for the volume of a cube is given by: \[ V = \text{edge length}^3 \] For a cube with an edge length of \( \frac{1}{2} \) inch: \[ V = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \text{ cubic inches} \]

  2. Total volume of 12 cubes: Now, we multiply the volume of a single cube by the total number of cubes (12): \[ \text{Total Volume} = 12 \times \frac{1}{8} = \frac{12}{8} = \frac{3}{2} \text{ cubic inches} \]

Thus, the volume of the right rectangular prism packed with 12 cubes is \(\frac{3}{2}\) cubic inches.

The correct answer is: \(\frac{3}{2}\) cubic inches.