Question #064a7

2 Answers
Aug 3, 2017

4422.6 pounds

Explanation:

"The concrete slab will be 12 feet 9 inches long, 9 feet 3 inches wide, and 3 inches thick"
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Laying out the information

  • 12 feet 9 inches is (12\cdot12)+9 since each foot is 12 inches. This gets you 144+9=153 inches for your length.
  • 9 feet 3 inches is (9\cdot12)+3 for the same reason. This gets you 108+3=111 inches for your width.
  • Your height (thickness of slab) is 3 inches.

Summarizing:
l=153 inches
w=111 inches
h=3 inches

Now find the volume of the slab by using the formula l\cdotw\cdoth, or 153xx111xx3=50949 cubic inches.

Converting
But the weight is 150 pounds per cubic foot, so you have to turn the inches into feet. Again, since each foot is 12 inches:
50949\text{ in}^3xx(1\text{ ft}^3)/(12xx12xx12\text{ in}^3)=50949/1728\text{ ft}^3=29.484\text{ ft}^3


Final steps
Now to solve for weight, multiply the cubic feet weight by 150 to get your answer.
29.484\text{ ft}^3xx(150\text{ pounds})/(1\text{ ft}^3)=4422.6 pounds

Aug 4, 2017

We will need to find the volume of the slab in cubic feet (ft^3), to compare it with the weight of the concrete which is also given in ft^3

V_(slab)=lxxwxxhto and 9i=.75ft and 3i=.25ft

Then: l=12.75ft, w=9.25ft, h=.25ft

Now: V_(slab)=12.75ftlxx9.25wxx.25h

V_(slab)=29.484ft^3

The weight of the slab is then: (V_(slab)=29.484cancel(ft^3))xx((150lb)/cancel(ft^3))=4422.6lb