Step 1: Hypothalamus's role in kidney function.
The hypothalamus, a vital brain region, governs homeostasis, particularly water and salt balance. It impacts kidney function by: Releasing antidiuretic hormone (ADH) through the posterior pituitary to enhance water reabsorption in collecting ducts. Regulating thirst and fluid intake, indirectly affecting glomerular filtration rate (GFR).
Step 2: Other options analyzed.
Option (A): Cerebellum. Incorrect. The cerebellum governs motor control and balance, not kidney function.
Option (C): Medulla oblongata. Incorrect. The medulla controls essential functions like heart rate and breathing but does not directly regulate kidney hormones.
Option (D): Cerebrum. Incorrect. The cerebrum is responsible for higher cognitive functions and does not regulate kidney function.
Step 3: Final determination.
The hypothalamus is the principal brain area controlling hormones such as ADH, crucial for kidney function. \[ \therefore \text{The correct answer is: Hypothalamus.} \]