Final answer:
Shannon is correct; the volume of a rectangular prism with the same base area and height as a rectangular pyramid is indeed three times larger. The volume of the pyramid is 60 units³, so the prism's volume would be 180 units³.
Step-by-step explanation:
Shannon is indeed correct in stating that a rectangular prism with the same base area and height will have a volume that is three times the size of the rectangular pyramid's volume. This is because the volume of a pyramid is one-third of the volume of a prism with the same base and height. The general volume formula for a pyramid is ⅓(base area × height), and for a rectangular prism, the volume formula is (base area × height).
The given volume of the rectangular pyramid is 60 units³. Thus, to find out the base area times the height of the prism, we can rearrange Equation 10.4.7 to give: base area × height = volume × 3, which results in a volume of 60 units³ × 3 = 180 units³.
Therefore, a rectangular prism with the same base area and a height of 5 units would indeed have a volume of 180 units³, validating Shannon's claim.