Final answer:
The volume of the prism is calculated by multiplying the volume of one single cube by the number of cubes that fit inside the prism, which totals to 18 cubic inches, not matching any of the provided options.
Step-by-step explanation:
The student is asking how to calculate the volume of a right rectangular prism, which is packed with cubes that have a side length of 1/4 inch. The prism has 12 cubes along its length and 8 cubes along its height. To find the volume of the prism, we first calculate the volume of a single cube, which is ¼ inch × ¼ inch × ¼ inch = 1/64 cubic inch. Since there are 12 cubes along the length and 8 cubes along the height, we assume that there are also 12 cubes along the width to make the prism fully packed. The total volume of the prism is then calculated by multiplying the volume of one cube with the total number of cubes, which is 12 × 8 × 12 = 1152 cubes. So the total volume is 1152 × 1/64 cubic inch = 18 cubic inches. This volume is not listed in the multiple-choice options provided, indicating a mistake in the question or the answers. However, of the provided options, 24 cubic inches (option b) is the closest to our calculation.