  Intersection bodies represent a remarkable class of geometric objects
associated with sections of star bodies and invoking
  Radon transforms, generalized cosine transforms, and the relevant Fourier
analysis. The main focus of this article is interrelation between generalized
cosine transforms of different kinds in the context of their application to
investigation of a certain family of intersection bodies, which we call
$\lam$-intersection bodies. The latter include $k$-intersection bodies (in the
sense of A. Koldobsky) and unit balls of finite-dimensional subspaces of
$L_p$-spaces. In particular, we show that restrictions onto lower dimensional
subspaces of the spherical Radon transforms and the generalized cosine
transforms preserve their integral-geometric structure. We apply this result to
the study of sections of $\lam$-intersection bodies. New characterizations of
this class of bodies are obtained and examples are given. We also review some
known facts and give them new proofs.
