How many cubic yards of concrete will need to be poured?

Mathematics
Tutor: None Selected Time limit: 1 Day

The concrete for a sidewalk is being poured outside the perimeter of a new subdivision, which is a 280 ft. by 720 ft. rectangle. The building code requires that the sidewalk be 5 feet wide and 8 inches deep. How many cubic yards of concrete will need to be poured? Explain your work step by step and why you took those steps. An average reader should be able to follow. 

Aug 30th, 2015

Thank you for the opportunity to help you with your question!

To best demonstrate this problem it is easier to first draw a rectangle. Label the left of the rectangle as 280 ft, and the top of the rectangle as 720 ft.

Next, you need to add five feet to the existing rectangle on all sides. So, draw another rectangle slightly bigger than the first triangle.

Note, that this changes the length and wide of the original rectangle. It adds an extra five to both sides, and an extra five to top and bottom.

Therefore you take the original 280ft +10ft=290 ft, and the original 720ft+10ft=730ft.

To calculate cubic yards : length in yards x width in yards x height in yards.

Once you convert each to yards: the cubic yards for the width is 2.95 cubic yards x 2 (since you have two widths)= 5.9 cubic yards

The cubic yards for the length is 7.43 cubic yards x 2 (since you have two lengths) = 14.86 cubic yards.

Add these two: 5.9 cubic yards + 14.86 cubic yards= 20.76 cubic yards in total.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 30th, 2015

* I made some calculator mistakes* I am so sorry 

Ft to yard conversion=

1ft= .3333333 yards

290 yards x .3333333= 96.7 yards

5 ft x .3333333= 1.67 yards

8 in = .67 ft

.67 ft x .3333333= .22 yards

76.7 yard x 1.67 yard x .22 yard= 35.52758 cubic yards x 2 = 71.05 cubic yards

730 ft x .3333333= 243.33 yards

243.333 x 1.67 yard x .22 yard= 89.4 cubic yards x 2= 178.8 cubic yards

243.33+178.8= 422.13 cubic yards

433 cubic yards in total.


Aug 30th, 2015

* Sorry, typing error. 423 cubic yards in total.

Aug 30th, 2015

I feel really bad, and I understand if you want to give me a bad review. I realized I made another typo and therefore error. To redeem myself, and hope to give you the final answer by a picture. Please look at the attachment, and let me know if you have any questions at all. 20150829_214040.jpg

Aug 30th, 2015

Hey, no problem! No need to feel bad, everyone makes mistakes. It's perfectly fine, considering you took your own time to help me with my question. No biggie. Thank you so much for the help! 

Aug 30th, 2015

Thank you for understanding, and I hope you enjoy the rest of your day. You are very welcome for the help.

Aug 30th, 2015

One question, why multiply by 1.67, when 8 inches is only .67 ft? 

Aug 31st, 2015

Just in case you do not see the chat for a while. I initially thought I was wrong again, when I was not.

1.67 yard is the measurement for the five feet.

Aug 31st, 2015

Ohhhhhhhhhhh!! I get it now... Haha, sorry :D. And thank you!

Aug 31st, 2015

It is absolutely no problem, I am glad I could clarify.

Aug 31st, 2015

Looking at this problem again, I believe there is a mistake. I forgot to account for the overlapping parts of the rectangle. Therefore the area is a little bit higher, but it is an easy mistake to fix. Let me draw you a picture of what I mean.

Sep 1st, 2015

Yea, I was wondering that, too, after multiplying during the conversions again

Sep 1st, 2015
image1(1).JPG

The answer actually didn't change that much. It is 248 cubic yards instead of 250.


Sep 1st, 2015

Wait... How? 

Sep 2nd, 2015

Nevermind

Sep 2nd, 2015

Wait, so while doing the math for the width, I don't need to do 290 ft x .33333? Because you used 280 ft x .33333, and then used that answer to move on to multiplying it by 1.67 and then by .22. So I can get rid of the 290 ft x .33333? 

Sep 2nd, 2015
Yes, exactly. It would be (280ft x .333333)(1.67)(.22)
Sep 2nd, 2015

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Aug 30th, 2015
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Aug 30th, 2015
Dec 6th, 2016
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