A standard steel plate is 4' wide, 8' long, 1" thick. If steel weighs 490 lbs/ft3, what is the total weight of this plate?

To find the total weight of the steel plate, we first need to calculate its volume and then multiply that volume by the density of steel.

The dimensions of the plate are given as:

• Width = 4 feet

• Length = 8 feet

• Thickness = 1 inch

Before calculating the volume, we must convert all dimensions to the same unit. Since the thickness is given in inches, we convert it to feet:

1 inch = 1/12 feet, so the thickness in feet is 1/12 feet.

Now, the volume ( V ) of the plate can be calculated using the formula for the volume of a rectangular prism:

[

V = \text{Width} \times \text{Length} \times \text{Thickness}

]

Substituting in the values we have:

[

V = 4 \text{ ft} \times 8 \text{ ft} \times \frac{1}{12} \text{ ft} = \frac{32}{12} \text{ ft}^3 = \frac{8}{3} \text{ ft}^3 \approx 2.6667 \text{ ft}^3

]

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