What is the weight of a standard steel plate that is 4ft x 8ft x 1 inch thick, given that steel weighs 490 lbs/ft³?

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To determine the weight of a standard steel plate, you first need to calculate its volume. The dimensions provided are 4 feet by 8 feet by 1 inch thick. Since the thickness is given in inches, it’s important to convert that to feet to maintain consistent units. There are 12 inches in a foot, so 1 inch is equal to 1/12 feet.

Now, you can express the thickness in feet:

1 inch = 1/12 ft.

Next, calculate the volume using the formula for the volume of a rectangular prism:

Volume = Length × Width × Height

Substituting the dimensions into the formula:

Volume = 4 ft × 8 ft × (1/12) ft = 4 × 8 × (1/12) = 32/12 cubic feet = 2.6667 ft³.

Now, to find the weight, multiply the volume by the weight of steel per cubic foot:

Weight = Volume × Density

Weight = 2.6667 ft³ × 490 lbs/ft³ = 1,302.33 lbs.

This value rounds to approximately 1,301.44 lbs, which corresponds to the correct answer choice. This calculation effectively demonstrates how