1. The problem asks to find the height $h$ of a cylindrical wheat silo given a rope of length 50 m inside it and the diameter of the silo is 12 m. 2. We model the situation as a right triangle where the rope is the hypotenuse, the height $h$ is one leg, and the diameter 12 m is the other leg. 3. Using the Pythagorean theorem for a right triangle: $$h^2 + 12^2 = 50^2$$ 4. Substitute the known values: $$h^2 + 144 = 2500$$ 5. Isolate $h^2$: $$h^2 = 2500 - 144$$ $$h^2 = 2356$$ 6. Take the positive square root (since height is positive): $$h = \sqrt{2356}$$ 7. Simplify the square root: $$h \approx 48.54$$ 8. Therefore, the height of the silo is approximately 48.5 meters. This completes the solution for the height $h$ of the silo using the Pythagorean theorem.