Table 3 Formulas for the total volume and lateral area of the tubular neighborhood

1

\({\pi}{r_{1}^{2}}(18{\pi}r_{1}-12r_{1} + 18{\pi}\rho _{1}+7 \frac{l}{2}-12\rho _{1})\)

2

\({\pi}{r_{2}^{2}}(186{\pi}r_{2}-124r_{2} + 186{\pi}\rho _{2}+63 \frac{ l}{4} -124\rho _{2})\)

Iteration #

Lateral area

1

\(2{\pi}{r_{1}}(3{\pi}r_{1}-12r_{1} + 3{\pi}\rho _{1}+7 \frac{l}{2}-12\rho _{1})\)

2

\(2{\pi}{r_{2}}(31{\pi}r_{2}-130r_{2} + 31{\pi}\rho _{2}+65\frac{ l}{4} -130\rho _{2})\)