How many solid spherical beads each of radius 5mm, can be made out of a solid rectangular block measuring 15cm by 13cm by 11cm

Question

How to find

Answer 1

Lets work with all of the lengths in mm.  Therefore the volume of the solid rectangular block is,

 

V = 150 mm x 130 mm x 110 mm = 2,145,000 mm³

 

So this is the amount of material that we have to make all of the spheres.  Keep in mind that the volume of a sphere is,

V = (4/3)*pi*r³ where r is the radius.

 

So how many solid spheres can we make from this much material?  If we let n = the number of spheres then,

 

n*(4/3)*pi*(5)³ = 2,145,000  --> number of spheres times volume per sphere = total volume

 

solving this for n gives n = 4096.65.  However, since talking about whole spheres we just truncate the result and we have that n = 4096 for the number of spheres that can be made.