Question

Identify each of the prisms for which the maximum amount of sand the prism can hold is 30 cubic inches. You must select two correct prisms.

A) Prism 1 and Prism 3
B) Prism 2 and Prism 4
C) Prism 1 and Prism 4
D) Prism 2 and Prism 3

Answer 1

The prisms for which the maximum amount of sand the prism can hold is 30 cubic inches is C) Prism 1 and Prism 4. (Option C)

Step-by-step explanation:

To determine the maximum amount of sand each prism can hold, we need to calculate their volumes. The formula for the volume of a prism is given by
`\(V = Bh\)`, where
`\(B\)` is the base area and
`\(h\)` is the height. In this case, the maximum amount of sand each prism can hold is 30 cubic inches.

Prism 1 has a base area of 10 square inches (B = 10 in²) and a height of 3 inches (h = 3 in). Therefore, the volume is
`\(V = Bh = 10 * 3 = 30\)`cubic inches, matching the given maximum.

Prism 4 has a base area of 15 square inches (B = 15 in²) and a height of 2 inches (h = 2 in). Again, the volume is
`\(V = Bh = 15 * 2 = 30\)` cubic inches, meeting the specified maximum.

Prisms 2 and 3 do not meet the requirement, as the calculated volumes exceed the given maximum of 30 cubic inches. This demonstrates the importance of considering both the base area and height when determining the capacity of prisms. In summary, the correct combination of prisms that can each hold a maximum of 30 cubic inches of sand is Prism 1 and Prism 4. (Option C)