  We study the spherical slice transform which assigns to a function on the
$n$-dimensional unit sphere the integrals of that function over cross-sections
of the sphere by $k$-dimensional affine planes passing through the north pole.
These transforms are well known when $k=n$. We consider all $1< k < n+1$ and
obtain an explicit formula connecting the spherical slice transform with the
classical Radon-John transform over $(k-1)$-dimensional planes in the
$n$-dimensional Euclidean space. Using this connection, known facts for the
Radon-John transform, like inversion formulas, support theorem, representation
on zonal functions, and others, can be reformulated for the spherical slice
transform.
