Question #064a7

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Question #064a7

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Answer 1 · 2017-08-03T21:15:49

$4422.6$ $4422.6$ 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 $(12 \cdot 12) + 9$ $(12\cdot12)+9$ since each foot is 12 inches. This gets you $144 + 9 = 153$ $144+9=153$ inches for your length.
9 feet 3 inches is $(9 \cdot 12) + 3$ $(9\cdot12)+3$ for the same reason. This gets you $108 + 3 = 111$ $108+3=111$ inches for your width.
Your height (thickness of slab) is $3$ $3$ inches.

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

Now find the volume of the slab by using the formula $l \cdot w \cdot h$ $l\cdotw\cdoth$ , or $153 \times 111 \times 3 = 50949$ $153xx111xx3=50949$ 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:
$50949 {in}^{3} \times \frac{1 {ft}^{3}}{12 \times 12 \times 12 {in}^{3}} = \frac{50949}{1728} {ft}^{3} = 29.484 {ft}^{3}$ $50949\text{ in}^3xx(1\text{ ft}^3)/(12xx12xx12\text{ in}^3)=50949/1728\text{ ft}^3=29.484\text{ ft}^3$

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

Answer 2 · 2017-08-04T02:08:28

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

$V_{s l a b} = l \times w \times h \to$ $V_(slab)=lxxwxxhto$ and $9 i = .75 f t$ $9i=.75ft$ and $3 i = .25 f t$ $3i=.25ft$

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

Now: $V_{s l a b} = 12.75 f t l \times 9.25 w \times .25 h$ $V_(slab)=12.75ftlxx9.25wxx.25h$

$V_{s l a b} = 29.484 f t^{3}$ $V_(slab)=29.484ft^3$

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

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Question #064a7

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