Expert: Paul Klarreich - 12/23/2006

Question
Thanks for the quick reply. A front end loader is a piece of heavy equipment that is often used on construction sites to load semis. I would say the bucket is shaped like a half circle. Ok the material I am loading weighs 700 lbs a cubic yard I get that by weighing a 1 cubic ft box then multiply that by 27. So with the bucket claimed to be 10cy that is how a get a bulk density. I need to figure out the cy of one bucket so if I had to figure the cubic yards of a half circle csn you help with that? I can measure winrows and LARGE piles but the bucket is not easy Thanks Chad
The text above is a follow-up to ...

-----Question-----
Ok here is something I have tried to figure out and cannot. I have a front end loader with a said 10cy bucket. There is NO WAY it holds 10cy with it being such an odd shape how do I figure out the cy of the bucket the easy way? my only other option is to get it level full dump it out and shovel all the mat. into a 1 cubic yard box and that does not sound like fun!I am not a math whiz and it is not my best trait. But if you could give me a simple formula that would be excellent. I have not been in a class room for 25 years so please try and keep is simple. You help is much needed and appreciated Thanks Chad
-----Answer-----
Questioner:  Chad
Category:  Calculus
 
Subject:  cubic yards of a triangle
Question:  Ok here is something I have tried to figure out and cannot. I have a front end loader with a said 10cy bucket. There is NO WAY it holds 10cy with it being such an odd shape how do I figure out the cy of the bucket the easy way? my only other option is to get it level full dump it out and shovel all the mat. into a 1 cubic yard box and that does not sound like fun!I am not a math whiz and it is not my best trait. But if you could give me a simple formula that would be excellent. I have not been in a class room for 25 years so please try and keep is simple. You help is much needed and appreciated

Thanks Chad  
......................................
Hi, Chad,

I am afraid that your statement: "with it being such an odd shape" is the clue:  Unless you know just what its shape is, and related dimensions, there is no way to determine its exact volume with some simple formula.  If it were a :

Cylinder: you could determine its radius and its height.
Pyramid: determine the area of its base and its height.
etc.
Now perhaps the figure is not as irregular as all that -- I don't know what a front-end loader looks like.  Perhaps it's quite regular and simple in shape.  If so, describe it as accurately as possible and let me know.

Aside from that, it looks as if the 'dump it out' method is all that's left.  And, by the way, when you say "shovel all the mat. into a 1 cubic yard box and that does not sound like fun!".  I know one 4-year old boy who might disagree.

And, one more thing -- volumes are frequently bigger than they 'look'.  Our spatial sense is not so good at that.  Even your little 15 by 10 by 8 second bedroom holds over 44 cubic yards.  If you don't believe me, ask your wife for permission to check it out.


Answer
Questioner:  Chad
Category:  Calculus
 
Subject:  cubic yards of an irregular figure
Question:  Thanks for the quick reply. A front end loader is a piece of heavy equipment that is often used on construction sites to load semis. I would say the bucket is shaped like a half circle.

>> Aha!  That's different.  Now we are in business.

Ok the material I am loading weighs 700 lbs a cubic yard I get that by weighing a 1 cubic ft box then multiply that by 27. So with the bucket claimed to be 10cy that is how a get a bulk density. I need to figure out the cy of one bucket so if I had to figure the cubic yards of a half circle csn you help with that? I can measure winrows and LARGE piles but the bucket is not easy Thanks Chad
...............................................

If the bucket (I guess you mean the 'working part' of the truck) is shaped that way, it is really a half-cylinder.  In that case, just do the following:

A. Measure the diameter of the cross-section of the bucket.  Take half of that and call it r, the radius.

B. Measure the length of the bucket.  Call that h, the height of the half-cylinder.

Since the volume of a cylinder is given by:

V = pi r^2 h,

just use your  r and h from the measurements, then take half of that in the end.  For example, if the bucket has a diameter of 8 feet across, and is 24 feet long, use r = 4, h = 24:

V = 0.5 * 3.14 (4)^2 (24)

= 603.2 cubic feet.

Now divide by 27, the number of cubic feet in a cubic yard, and you get:

V = 22.3 cubic yards.

Not as small as you thought.