A rectangular prism has a volume of 8 cubic yards. Assume the dimensions are whole numbers. What dimensions yield a prism with the greatest surface area? the least surface area? (1 point)
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To find the dimensions that yield a prism with the greatest surface area, we want to minimize the individual dimensions. If the dimensions are whole numbers, the smallest possible values for the dimensions would be 1, 1, and 8.
So, the smallest surface area of the prism would be achieved when the dimensions are 1 yard, 1 yard, and 8 yards.
To find the dimensions that yield a prism with the least surface area, we want to maximize the individual dimensions. The largest possible values for the dimensions while still maintaining a volume of 8 cubic yards would be 2, 2, and 2.
So, the largest surface area of the prism would be achieved when the dimensions are 2 yards, 2 yards, and 2 yards.
Therefore, the smallest surface area is 54 square yards and the largest surface area is 24 square yards.