Given volume of the rectangualr plate is equal to volume of circular rod (cylinder).

diameter of the circular rod is 8 inches

so, radius is 4 inches

length of the rectangualr plate is 8 inches

breadth of the rectangualr plate is 11 inches

width of the rectangualr plate is 2 inches

volume of the rectangle is length*breadth*width

volume of the cylinder is PI*radius*radius*length

so,

volume of the rectangle = volume of the cylinder

8*11*2 = (22/7)*4*4*length

length = 8*11*2*(7/22)*(1/4)*(1/4)

length = 1232/352

length = 3.5inches