Number, Amount Needed

[Guest]

A number of concrete fence posts are to be constructed. The posts will be 8 feet in length and taper evenly from 5 x 5 inches at the bottom to 3 x 3 inches at the top. Calculate number of posts that can be produced and amount of sand and gravel needed.

8 bags of cement are available.

The posts are made from a 1 - 2 - 3 mixture of cement, sand, and gravel/rocks.

I know concrete is measured by the cubic yard.

Let P = Number of posts
Let S = Amount of sand
Let G = Amount of gravel

How do I begin ?

[Guest]

Assume the mix is 1 : 2 : 3 by volume
That is say.....1 cubic inch cement : 2 cubic inches sand : 3 cubic inches gravel.......thats 6 cubic inches all together.

so 1/6 cement, 2/6 = 1/3 sand, 3/6 = 1/2 gravel.

need to know the size of a bag of cement in cubic inches..??? then work out volume of sand and gravel needed

find volume of 1 post.....then work out the volume of each cement, sand, and gravel

divide the amount for 1 post into total to get how many

[Guest]

A chart related to the problem only indicates for a 1-2-3 mixture, 7 bags of cement, 14 cu. ft. of sand and 21 cu. ft. of gravel are required for 1 cu. yard of concrete. How would 1 bag be calculated ?

[Guest]

So didn't get all the info.............

You don't need to know volume in 1 bag as such.......
You know from the chart that for a 1-2-3 mixture, 7 bags of cement, 14 cu. ft. of sand and 21 cu. ft. of gravel are required for 1 cu. yard of concrete. So you will have to calculate or read from the chart how many cu.yards 8 bags will make assuming there is also enough sand and gravel available.
The question says 8 bags of cement are available and doesn't mention sand and gravel.

When you have worked out how much concrete you can make then divide the volume of 1 post into it to find how many posts

[Guest]

Sorry for the omission.

[Guest]

Volume of one post :

8 ft. x 5 in. x 3 in.

8 x .4166 x .25 = .83332 cu. ft.

Due to the chart indicating data for only 7 bags of cement for the 1-2-3 mixture, then 8 bags will be slightly more.

I don't know how to calculate for the 8 bags.

[Guest]

.83332 x 14 = 11.66648 = 11.67 cu. ft. of sand

.83332 x 21 = 17.49972 = 17.5 cu. ft. of gravel

I believe I miscalculated in a step.

The answers are by using the 7 bags of cement data. The data will be slightly higher for 8 bags as stated in previous post.

How do I calculate for the 8 bags ?

[Guest]

The posts are tapered from 5x5 to 3x3 and 8ft long.....so your volume for 1 post is wrong......

Also if 7 bags cement make 1 cu yard of concrete.....how much would 8 bags make....???

[Guest]

And if you haven't noticed the question is all about ratios and proportions.................

[Guest]

1/7 = x/8
7x = 8
7x/7 = 8/7
x = 1.142 cu. ft. of cement

7/14 = 8/x
7x = 112
7x/7 = 112/7
x= 16 cu. ft. of sand

7/21= 8/x
7x/7 = 168/7
x= 24 cu. ft. of gravel

8 x 5 x 2 x 3
8 x .4166 x .166 x .25 = .1383 = .134 cu. ft. (volume of post)

1.142/.134 = 8.522 = 8.5 posts

I think I miscalculated again for posts.

[Guest]

Did you read the last post.......where have you calculated anything using ratios..????

What is "x" where did it come from.............

Are you working in cu inches , cu feet, or cu yards...............

how do you calculate the volume of a tapered solid object such as a post........

You have just put down a conglomeration of number without any reasoning whatsoever.....

You are not even using the facts given in the question or trying to put them together in any logical way.....

You say you have miscalculated again......then why do you not correct it and post again.....

[Guest]

I used proportions to obtain amounts for 8 bags using data for 7 bags:


Let c = amount of cement-

1/7 = c/8
7c = 8
7c/7 = 8/7
c = 1.142 cu. ft. of cement

Let s = amount of sand-

7/14 = 8/s
7s = 112
7s/7 = 112/7
s= 16 cu. ft. of sand

Let g = amount of gravel-

7/21= 8/g
7g/7 = 168/7
g= 24 cu. ft. of gravel


Posts are constructed using 1 : 2 : 3 mixture - 1 part cement, 2 parts sand, 3 parts gravel.

I don't know how to apply the ratio in this type problem or calculate volume of a tapered object.

[Guest]

You are not trying to apply any logic to the problem or follow what was done in other problems before............
You need to break it down into steps following the info given in the question......
And work out bits as you go along and so progress through the problem....
If you don't understand this level of reasoning you would need to start with simple questions and work your way up...
But as you will see the solution given below is fairly basic and straight forward if you sit down and work your way through it.
Also the numbers are so simple you should not even need a calculator.....
I hope it is of some help to you.....but you need to sit down and work logically through it, don't just read it, then do some even simpler problems to come to terms with the processes involved...........

Solution.........
the posts are tapered as a pyramid.....with the top point cut off.......
Taper of posts......width is reduced by 2 inches over 8 feet, that is 1 inch per 4 feet length.
To work out volume of pyramid need to know full height to the point, or Zero width,
So if post was full pyramid the 5 x 5 base would taper to 0 (zero) inches at a rate of 1 inch per 4 feet.
So that is 4 x 5 = 20 feet...or 20 x 12 inches....we will work out the full volume (20 feet) and then subtract off the top (12 feet) pointed bit.

Volume full pyramid = 1/3 x area of base x height.......1/3 x (5 x 5) x (20 x 12) = 2000 cu inches
Volume of top point = 1/3 x (3 x 3) x (12 x 12) = 432 cu inches.
Volume of post = 2000 - 432 = 1568 cu inches

Concrete ......7 bags make 1 cu yard or 3 x 3 x 3 = 27 cu feet or 27 x 12 x 12 x 12 = 46656 cu inches
So 8 bags will make 46656 / 7 x 8 = 53321 cu inches.

So number of posts = 53321 / 1568 = 34 posts................

The amount of each material is......

Cement......1/6 x 53321 = 8887 cu inches = 5.143 cu feet....which we know is 8 bags.

Sand ...... 1/3 x 53321 = 17774 cu inches = 10.286 cu feet

Gravel .....1/2 x 53321 = 26661 cu inches = 15.429 cu feet

Which is a ....... ( 1 : 2 : 3 ) mix of ( cement : sand : gravel ).

.......................Simple.............................