Question

A cylindrical cardboard mailing tube has a diameter of 5 in. and a height of 30 in. A total of 30% of the tube’s capacity is filled with spherical packing foam. Each foam sphere has a diameter of 0.6 in. Approximately how many pieces of foam are in a tube?

Answer 1

First is to get the volume of the cylinder.
Volume = pi * r^2 * H
Volume = 3.1416 * (5/2)^2 * 30
Volume = 589.05 in^3

30% is already filled.
Filled Space = 589.05 * 0.30
Filled Space = 176.715 in^3
Empty Space = 412.335 in^3

Next, get the volume of the sphere.
V = (4/3)*pi*r^3
V = (4/3)*pi*(0.6/2)^3
V = 0.1130976 in^3

Number of foams = Filled Space / V
Number of foams = 176.715 / 0.1130976 
Number of foams = 1562 Foams