  We give a positive solution for the hyperplane conjecture of quotient spaces
F of $L_p$, where $1<p\kll\infty$. \[ vol(B_F)^{\frac{n-1}{n}} \kl c_0 \pl p'
\pl \sup_{H \p hyperplane} vol(B_F\cap H) \pl.\] This result is extended to
Banach lattices which does not contain $\ell_1^n$'s uniformly. Our main tools
are tensor products and minimal volume ratio with respect to $L_p$-sections.
