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# Advanced Math/Number, Amount Needed Follow-up

Question
A chart related to the problem only indicates for a 1-2-3 mixture with 7 bags of cement, 14 cu. ft. of sand and 21 cu. ft. of gravel are required for 1 cu. yard of concrete. Maybe that will help.  Thanks again.

Let θ be the base angle of the post, then tanθ = 96.
https://www.flickr.com/photos/dwread/15091183430/ (drawing not to scale)

Now I'll switch to working in feet. (I'll use fractions to avoid rounding errors.)
The post is 8 feet high, its base is (5/12) ft by (5/12) ft, and its top is ¼ ft by ¼ ft.

The post is the bottom section of a square pyramid.
https://www.flickr.com/photos/dwread/15092592898/ (drawing not to scale)
height of pyramid = (5/24)tanθ = 20 ft
volume of pyramid = (⅓)b²h = (⅓)(5/12)²·20 ≅ 125/108 ft³

The top section of the pyramid is a smaller pyramid. It is 20-8 = 12 ft high and its base is ¼ ft by ¼ ft.
volume of smaller pyramid = (⅓)b²h = (⅓)(¼)²·12 = ¼ ft³
volume of post = 125/108 - ¼ = 49/54 ft³

7 bags of cement are required for 1 yd³ = 27 ft³ of concrete.
8 bags  × 27 ft³/(7 bags) = 216/7 ft³
Using 8 bags of cement, you can make 216/7 ft³ of concrete.

216/7 ft³ × 1 post/(49/54 ft³) ≅ 34.00583 posts
You can make 34 posts, which will require 34 posts × 49/54 ft³/post = 833/27 ft³ of concrete.

Each cubic foot of concrete contains 7/27 bag of cement, 14/27 ft³ of sand, and 21/27 = 7/9 ft³ of gravel. So, to make 34 posts you will use
833/27 ft³ concrete × 7/27 bag cement/(1 ft³ concrete) ≅ 7.999 bag cement
833/27 ft³ concrete × 14/27 ft³ sand/(1 ft³ concrete) ≅ 15.997 ft³ sand
833/27 ft³ concrete × 7/9 ft³ sand/(1 ft³ concrete) ≅ 23.996 ft³ gravel
You can probably round that to 8 bags of cement, 16 cubic feet of sand, and 24 cubic feet of gravel.
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