Let Bⁿp denote the unit ball in lⁿp with p ≥ 1. We prove that Voln₋₁(H ∩ Bnp) ≥ (Voln(Bnp))⁽ⁿ⁻¹⁾ for any (n−1)-dimensional subspace H of Rⁿ. This is a consequence of bounding
the isotropy constant of Bⁿp above by 1/√12 and we show that one can replace 1/√12 by a possibly
smaller number for n ≥ 2.