Final answer:
The volume of a rectangular prism with a square base and given areas and height is calculated by multiplying the base area by the height. None of the listed options is correct; the actual volume is 1.12 m³ or 28/25 m³.
Step-by-step explanation:
To calculate the volume of a rectangular prism, use the formula Volume = length × width × height. The problem states that the prism has a square base with an area of 2 4/5 m², which translates to 14/5 m² since 2 4/5 = 2 + 4/5 = 10/5 + 4/5 = 14/5. The height of the prism is 2/5 m.
First, since the base is square and we know its area, the length and width are the same, and therefore, the length and width are the square root of the base area. However, we don't actually need to calculate the sides since the volume formula for a square base can be simplified to Volume = base area × height.
Then, we can calculate the volume:
Volume = (base area) × (height) = (14/5 m²) × (2/5 m) = (14 × 2)/(5 × 5) m³ = 28/25 m³ = 1 3/25 m³, which simplifies further to 1 3/25 m³ = 1 + 3/25 m³ = 25/25 + 3/25 m³ = 28/25 m³ or 1.12 m³.
Therefore, the correct answer is none of the listed options a, b, or c. It's 1.12 m³ or 28/25 m³.