Daniel buys a block of clay shaped like a cube with edges that are 10 inches long to use in his art class. He decides to cut the clay into two pieces. He places a wire across the diagonal of one of the faces of the cube, as shown in the figure. Then he pulls the wire straight back to create two congruent chunks of clay. Daniel wants to make one chunk of the clay into spheres with a diameter of 4 inches. What is the maximum number of spheres he can make from the half that he uses?