L= ∫ ^( β)_( α )sqrt(ρ^(2)( φ )+(ρ`( φ ))^2)d φ
ρ=3*(1-cos φ )
ρ`=3*(sinx φ )
ρ^2+(ρ`)^2=9*(1-cos φ )^2+9sin^2 φ =18-18cos φ =36sin^2( φ /2)
sqrt(ρ^(2)( φ )+(ρ`( φ ))^2)=6sin( φ/2)
L= ∫ ^(2π)_( 0 )6sin(φ/2)dφ =12(-cos( φ /2))|^(2π)_(0)=
=-24*(cosπ-cos0)=48