Rufus leak stores his collection of cannonballs in cubical that have no tops. The volume of each cube equals its surface area (units are in cubic feet). The volume of each cannonball equals its surface area (units are in cubic inches). How many cannonballs can Rufus fit into each box?

For the answer to the question above, I'll show the computation below.

V (cube) = s^3

SA (cube with no top) = 5s^2

s^3 = 5s^2

s = 5

V = 125 sq ft = 216,000 sq in

V (cannonball) = (4/3) πr^3

SA (cannonball) = 4πr^3

(4/3) πr^3 = 4πr^2

r = 3

V = 36π sq in

Packing of spheres in a cube is yielding up to 74% with remainder as space between the spheres. It can be achieved by placing the 2nd row of spheres in the crevices between adjoining first row spheres.

216,000 / 36π = 6,000/π

(6000/π) *.74 = 1414 spheres can be fit "in" each box.