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marble of diameter 10mm each are to be arranged on a flat surface so that their center lie with the area enclosed by four linws of length each 40mm. sketch the arrangement that will give the maximum number of marble per unit area, that can be enclosed in this manner and deduce the expression to calculate it.

marble of diameter 10mm each are to be arranged on a flat surface so that their center lie with the area enclosed by four linws of length each 40mm. sketch the arrangement that will give the maximum number of marble per unit area, that can be enclosed in this manner and deduce the expression to calculate it.

Grade:11

1 Answers

Anwesh
21 Points
6 years ago
CD=10sin60∘=10×3–√210sin⁡60∘=10×32⇒53–√⇒53Area of square having spherical marbles in it.⇒40×10−1×40×10−1cm2⇒40×10−1×40×10−1cm2⇒16cm2⇒16cm2The maximum no. of spheres of 10mm diameter in hcp packing can be seen.Total length covered by spheres =5+4×CD5+4×CD=5+4×10sin60∘=5+4×10sin⁡60∘=5+4×53–√=40=5+4×53=40 mmMaximum number of spheres =14(full) + 8(half) = 18∴∴ Number of spheres per cm2=1816cm2=1816=1.125

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