1. The problem is to find the volume of a cylinder with a base radius of 50 cm and a height of 5 cm. 2. The formula for the volume $V$ of a cylinder is: $$V = \pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height. 3. Substitute the given values $r = 50$ cm and $h = 5$ cm into the formula: $$V = \pi (50)^2 (5)$$ 4. Calculate the square of the radius: $$50^2 = 2500$$ 5. Multiply the values inside the formula: $$V = \pi \times 2500 \times 5$$ 6. Simplify the multiplication: $$V = \pi \times 12500$$ 7. Use the approximation $\pi \approx 3.14159$ to find the volume: $$V \approx 3.14159 \times 12500 = 39269.9$$ 8. The volume of the cylinder is approximately: $$\boxed{39269.9 \text{ cm}^3}$$ This means the cylinder holds about 39269.9 cubic centimeters of space.