How many baseballs will fit in 16 cubic feet?

Answer 1

That depends a whole lot on the shape of those 16 cubic feet, and on the size of the baseballs (which vary slightly). You should see here:

http://www.daviddarling.info/encyclopedia/C/Cannonball_Problem.html
http://mathworld.wolfram.com/CannonballProblem.html

You'd basically just adapt that to whatever shaped space you're trying to put them in.

Answer 2

By definition, a baseball is "9 to 9.25 inches in circumference." That means that the diameter is between 2.864788975 and 2.944366447 inches (an average of 2.904577711 inches).

In three dimensional Euclidean space, let us consider a plane with a compact arrangement of spheres on it. if we consider three neighbouring spheres, we can put a fourth sphere in the hollow between the three bottom spheres. If we do this "everywhere", we create a new compact arrangement. The third layer can superimpose to the first one, or the spheres can be upon a hollow of the first layer. There are thus three types of planes, called A, B and C.

Gauss proved these arrangements have the highest density amongst the regular arrangements.

The two most common arrangements are called cubic close packing (or face centred cubic) — ABCABC… alternance — and hexagonal close packing — ABAB… alternance. But all combinations are possible (ABAC, ABCBA, ABCBAC, etc.). In all of these arrangements each sphere is surrounded by 12 other spheres, and both arrangements have an average density of

pi/sqrt(18) = 0.74048 approximately

That is the balls will fill about 0.74048(16 cubic feet) = 11.84768 cubic feet of the 16 cubic feet.

circumference: 9 in. < c < 9.25 in.
9 < 2(pi)r < 9.25 in.
radius: 9 / (2(pi)) in. < r < 9.25 / (2(pi)) in.
volume: (4 / 3)(pi)[9 / (2(pi))]^3 in^3 < v < (4 / 3)(pi)[9.25 / (2(pi))]^3 in^3
12.31052381 in^3 < v < 13.36516124 in^3

note: 1728 in^3 = 1 ft^3 and 27,648 in^3 = 16 ft^3.
0.74048(27,648 in^3) = 0.74048(16 ft^3)
20472.79104 in^3 = 11.84768 ft^3

1663.0 > balls > 1531.8

Answer: There are between 1,532 and 1,663 balls in a volume of 16 cubic feet.

Answer 3

Baseballs have a circumference not less than 9" nor more than 9 1/4", which gives them a diameter range of 2.865" to 2.944" The answer to your question depends on the configuration of the 16 ft^3. Using cubic close-pack, the maximum possible number of baseballs that can fit into 16 ft^2 is int(16/0.013606) = 1,175

Answer 4

1024 baseballs

This is assuming that the baseball is at most 3" in diameter and that the 16 cubic feet are arranged to fit the maximum number of baseballs.

The baseballs are between 2 7/8" and 3" in diameter according to the following website.

Answer 5

The answer also depends on whether or not you intend those baseballs to remain intact. If not, the configuration of the 16 cu ft dont matter