Question

Question #064a7

Answer 1

`4422.6` pounds

Explanation:

"The concrete slab will be 12 feet 9 inches long, 9 feet 3 inches wide, and 3 inches thick"
computer
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.

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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`

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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

Answer 2

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`