Question

A cylindrical cardboard mailing tube has a diameter of 90 mm. and a height of 600 mm. A total of 20% of the tube’s capacity is filled with spherical packing foam. Each foam sphere has a radius of 15 mm.

Approximately how many pieces of foam are in the tube?
Use 3.14 to approximate pi and express your answer as a whole number.

Answer 1

Calulate Cylinder Volume: remember; Vcyl = 3.14(r)2h

Vcyl = 3.14 (45mm)2 600 mm

Vcyl = 3.14 (2025mm2) 600mm Vcyl = 3815100 mm3 or 3.8 x106 mm3

Next calculate the percentage of volume taken up by styrofoam balls

3815100 x 20/100 = 763020 Vstyroballvol = 763020mm3

{as a check calculate}

80% 3815100 x 80/100 = 3052080 mm3

20% 3815100 x 20/100 = 763020 mm3

100% = 80% + 20% = 3815100 mm3

Now calculate the Volume of the Sphere: Vsphere = 4/3*3.14*(r)3

Vsp = 4/3*3.14*(15mm)3 Vsp = 4/3*3.14*(3375) Vsp = 14130 mm3

for 1 stryofoam ball

Lastly divide the amount of 20% vol of cylinder by one ball volume

763020mm3 / 14130mm3

= 54 styrofoam balls will fill or are in the tube. Answer