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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 :

firenlaw

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

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