Step 1 :Given the volume of rectangular pyramid A is 148 cubic inches and the scale factor is 4.
Step 2 :Use the formula for the volume of a pyramid after dilation: Volume of pyramid B = Volume of pyramid A * (scale factor)^3
Step 3 :Calculate the volume of pyramid B: \(148 * (4)^3\)
Step 4 :\(\boxed{9472}\) cubic inches is the volume of rectangular pyramid B.