Given a graph G and a vertex subset S of V(G), the broadcasting time with respect to S, denoted by b(G,S), is the minimum broadcasting time when using S as the broadcasting set. And the k-broadcasting number, denoted by bk(G), is defined by bk(G)=min{b(G,S)|S⊆V(G),|S|=k}.Given a graph G and two vertex subsets S, S′ of V(G), define d(v,S)=minu∈Sd(v,u), d(S,S′)=min{d(u,v)|u∈S, v∈S′}, and d(G,S)=maxv∈V(G)d(v,S) for all v∈V(G). For all k, 1⩽k⩽|V(G)|, the k-radius of G, denoted by rk(G), is defined as rk(G)=min{d(G,S)|S⊆V(G), |S|=k}.In this paper, we study the relation between the k-radius and the k-broadcasting numbers of graphs. We also give the 2-radius and the 2-broadcasting numbers of the grid graphs, and the k-broadcasting numbers of the complete n-partite graphs and the hypercubes.