Question

Suppose you harvested a large crop of grain this year. The grain is now in a pile and takes up an area of 50 m2 and is 2 m high. You have a silo that has an area of 15 m2 that is 3 m high. Will all of the grain fit in this silo? If not, how much of the grain will remain outside of the silo? Show your work

Answer 1

I'm pretty sure that the silo has the shape of a cylinder.
So its volume is

          (area of the base) x (height)  =  (15 m²) x (3m) = 45 m³ .


I'm going to assume that the pile has taken the shape of a cone
on the ground, so its volume is

                 (1/3) x (area of the base) x (height)

              = (1/3) x (50m²) x (2m) = 33-1/3 m³  .

The whole answer to the question rests on the exact shape of
the pile of grain on the ground.  It could really help if somebody
could take a picture of the pile, so we could study the picture
here in Chicago, and estimate how closely the shape of the
pile resembles a cone.

If my assumption is valid, and the volume of grain in the pile
can be accurately calculated as the volume of a cone with the
same dimensions as the pile, then the grain will all fit in the silo
with no problem.  The silo will still be only 74% full, and it'll still
have room for another  11-2/3 m³  of grain.  

But if, say, the grain got wet and sticky as it was being poured
onto the pile, and the pile took the shape of a huge brick, then
its volume is  (area of the base) x (height) = 100 m³ .
If that's the shape of the pile, then only 45% of it will fit into the
silo.  The silo will be full and there'll still be 55 m³ of grain left
out on the ground to rot.

With the information that they sent to us up here in Chicago,
we simply don't know.