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Magnetic moment of a current carrying coil is given by

m = NIA

where, N is number of turens

I is the current flowing through coil

A is the cross sectional area of the coil

For coil in circular shape, A = πr^2

Hence, m1 = NI (πr^2)

For coil in square shape, A = a^2

Hence, m2 = NI (a^2)

Taking ratio of bothn we get,

m1/m2 = [NI (πr^2)]/[NI (a^2)]

Therefore, m1/m2 = (πr^2)/(a^2)