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"
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.

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#