A self-adjusting firestopping sleeve apparatus positionable through an aperture in a construction barrier for a penetrating member to extend therethrough, comprising: a first firestopping pad comprised of a first pad resilient foam including a pad intumescent component, the first firestopping pad having a first convex surface; a first projecting block comprised of a first block resilient foam including a block intumescent component and attached to the first convex surface of the first firestopping pad such that an equal amount of the first projecting block is located on each side of an apex of the first firestopping pad, the first projecting block (i) has a first contact surface spaced from the first convex surface of the first firestopping pad and (ii) extends only over a middle portion of the first convex surface; a second firestopping pad comprised of a second pad resilient foam including the pad intumescent component, the second firestopping pad having a second convex surface; a second projecting block comprised of a second block resilient foam including the block intumescent component and attached to the second convex surface of the second firestopping pad such that an equal amount of the second projecting block is located on each side of an apex of the second firestopping pad, the second projecting block (i) has a second contact surface spaced from the second convex surface of the second firestopping pad and (ii) extends only over a middle portion of the second convex surface; the first and second firestopping pads positioned with the first convex surface and the second convex surface facing opposite one another such that the first and second contact surfaces are in contact to form a sealing abutment seam; wherein the first and second firestopping pads and the first and second projecting blocks define a confinement area for receiving the penetrating member to extend longitudinally therethrough; wherein at least one of the first and second firestopping pads is arched toward the other firestopping pad (24, 26); wherein each of the first and second projecting blocks has a trapezoidal configuration; wherein the first contact surface of the first projecting block is planar and has a width equal to a width of the first firestopping pad, the second contact surface of the second projecting block is planar and has a width equal to a width of the second firestopping pad; wherein the configuration of the first and second firestopping pads and the first and second projecting blocks causes an adequate compression force for accommodating a self-adjusting sealing of the penetrating member extending through the abutment seam. a first firestopping pad comprised of a first pad resilient foam including a pad intumescent component, the first firestopping pad having a first convex surface; a first projecting block comprised of a first block resilient foam including a block intumescent component and attached to the first convex surface of the first firestopping pad such that an equal amount of the first projecting block is located on each side of an apex of the first firestopping pad, the first projecting block (i) has a first contact surface spaced from the first convex surface of the first firestopping pad and (ii) extends only over a middle portion of the first convex surface; a second firestopping pad comprised of a second pad resilient foam including the pad intumescent component, the second firestopping pad having a second convex surface; a second projecting block comprised of a second block resilient foam including the block intumescent component and attached to the second convex surface of the second firestopping pad such that an equal amount of the second projecting block is located on each side of an apex of the second firestopping pad, the second projecting block (i) has a second contact surface spaced from the second convex surface of the second firestopping pad and (ii) extends only over a middle portion of the second convex surface; the first and second firestopping pads positioned with the first convex surface and the second convex surface facing opposite one another such that the first and second contact surfaces are in contact to form a sealing abutment seam; wherein the first and second firestopping pads and the first and second projecting blocks define a confinement area for receiving the penetrating member to extend longitudinally therethrough; wherein at least one of the first and second firestopping pads is arched toward the other firestopping pad (24, 26); wherein each of the first and second projecting blocks has a trapezoidal configuration; wherein the first contact surface of the first projecting block is planar and has a width equal to a width of the first firestopping pad, the second contact surface of the second projecting block is planar and has a width equal to a width of the second firestopping pad; wherein the configuration of the first and second firestopping pads and the first and second projecting blocks causes an adequate compression force for accommodating a self-adjusting sealing of the penetrating member extending through the abutment seam.