You are given marble of diameter 10 mm . They are to be placed such that their centres are lying in a square bounded by four lines each of length 40 mm . The maximum number of marbles which may be pla

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You are given marble of diameter 10 mm . They are to be placed such that their centres are lying in a square bounded by four lines each of length 40 mm . The maximum number of marbles which may be placed inside this area is

TestHub · Accepted Answer

For maximum packing we should take HCP of two dimension

$P.F. = \frac{\frac{1}{6} π r ^{2} \times 3}{\frac{3}{4} ( 2 r ) ^{2}} = \frac{π}{2 3}$

$\frac{π}{2 3} = \frac{n π ( 5 ) ^{2}}{( 40 ) ^{2}}$ $n = \frac{64}{2 3} = \frac{32 3}{3} = \frac{32 \times 1.732}{3} = 18.47$

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JEE Main + Advanced (1 year 12th class)