(N/A) Cockroaches are dioecious,and both sexes have well-developed reproductive organs.
$(i)$ Male reproductive system: The male reproductive system consists of a pair of testes,one lying on each lateral side in the $4^{th}-6^{th}$ abdominal segments.
From each testis,a thin vas deferens arises,which opens into the ejaculatory duct through the seminal vesicle. The ejaculatory duct opens into the male gonopore situated ventrally to the anus.
$A$ characteristic mushroom-shaped gland is present in the $6^{th}-7^{th}$ abdominal segments,which functions as an accessory reproductive gland. Another long and flat gland,the conglobate gland,is located on the ventral side of the ejaculatory duct and acts as an accessory reproductive gland. Its secretion forms a hard coating around the sperm bag.
The external genitalia are represented by male gonapophysis or phallomeres (chitinous asymmetrical structures surrounding the male gonopore).
The sperms are stored in the seminal vesicles and are glued together in the form of bundles called spermatophores,which are discharged during copulation.
$(ii)$ Female reproductive system:
The female reproductive system consists of two large ovaries lying laterally in the $2^{nd}-6^{th}$ abdominal segments.
Each ovary is formed of a group of eight ovarian tubules or ovarioles containing a chain of developing ova.
Oviducts of each ovary unite into a single median oviduct (also called vagina) which opens into the genital chamber. $A$ pair of spermatheca is present in the $6^{th}$ segment,which opens into the genital chamber.
Egg cells enter the genital chamber during mating and are fertilized by sperm cells.
Collateral glands present in the female cockroach secrete substances that form the ootheca.
Fertilized egg cells are encased in capsules called oothecae. An ootheca is a dark reddish to blackish-brown capsule,about $8 \ mm$ long. They are dropped or glued to a suitable surface,usually in a crack or crevice of high relative humidity near a food source.
On average,females produce $9-10$ oothecae,each containing $14-16$ eggs.
The development of $P. \ americana$ is indirect,meaning it proceeds through a nymphal stage.
The nymph resembles the adult insect. The nymph grows by moulting about $13$ times to reach the adult form. The next-to-last nymphal stage has wing pads,but only adult cockroaches have wings.