Final answer:
The EPA is the government agency that develops and approves topical pesticides as it administers the FIFRA and oversees pesticide registration in the U.S.
Step-by-step explanation:
The government agency responsible for developing and approving topical pesticides is the Environmental Protection Agency (EPA). The EPA administers the Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) and is in charge of the registration of all pesticides legally sold in the United States. This contrasts with the roles of other agencies such as the FDA, which is responsible for the regulation and supervision of food safety, pharmaceuticals, and other health-related products.