If a 1'x1'x1/4" piece of concrete weighs 10 lbs, how much does a 4'x20'x1' slab weigh?

• A. 1,600 lbs
• B. 3,200 lbs
• C. 6,400 lbs
• D. 8,000 lbs

Answer: (B)

Concrete weight scales with volume: the same material has the same weight per unit volume, so you can convert a small sample’s weight into a weight per cubic foot and then apply that to the larger slab.

From the sample piece: a 1 ft by 1 ft by 1/4 inch block weighs 10 lb. Its volume is 1 × 1 × (1/48) = 1/48 ft³, so the weight density is 10 lb per 1/48 ft³, which equals 480 lb per cubic foot.

The slab is 4 ft by 20 ft by 1 inch thick. The thickness in feet is 1/12 ft, so its volume is 4 × 20 × 1/12 = 80/12 ≈ 6.6667 ft³. Multiply by the density: 6.6667 × 480 ≈ 3,200 lb.

So the slab weighs 3,200 pounds. If the thickness were 1 foot, the weight would be 38,400 lb, illustrating how sensitive the weight is to thickness.