Question

Marbles of diameter 10 mm are to be placed such that their centers are lying in a square bound by 4 lines each of lenght 40 mm find the arrangement of marbles in a plane sk that maximum no of marbles can be placed inside the area

Answer 1

Answer:

1.125

Step-by-step explanation:

Diameter of marbles = 10mm

Length of the line of square = 40mm

Line CD= 10sin60° =10×√3/2

= 5√3

Area of square having spherical marbles in it -  

= 40×10−1×40×10−1 cm²

= 16cm2

The maximum number of spheres of 10mm diameter in the packing will be there.

Thus, the total length covered by spheres  = 5+4×CD

= 5+4×10sin60∘

= 5+4×5√3

=40 mm

Maximum number of spheres =14(full) + 8(half) = 18

Therefore the number of spheres per cm² =18/16 =1.125