Final answer:
The height of the cylinder can be found by using the surface area formula A = 2πrh + 2πr². Given the radius (r = 5 m) and surface area (A = 439.8 m²), and after accounting for significant figures, the height (h) is calculated to be approximately 12.44 m.
Step-by-step explanation:
To find the height of a cylinder when given the radius and the surface area, we use the formula for the surface area of a cylinder, which is A = 2πrh + 2πr², where A is the surface area, r is the radius, and h is the height.
Let's plug in the given values: A = 439.8 m² and r = 5 m. Replacing these values, we get 439.8 m² = 2π(5 m)h + 2π(5 m)². Simplifying this equation by calculating 2π(5 m)² yields the area of the two circular bases of the cylinder, which is 50π (square meters). Subtracting this value from the total surface area gives us the surface area of the cylindrical part: 439.8 m² - 50π m² = 2π(5 m)h).
We then divide the remainder by 2π(5 m) to isolate h, which gives us the height: h = (439.8 m² - 50π m²) / (2π(5 m)). Calculating with the value of π as approximately 3.14159, we find that the height of the cylinder is approximately 12.44 m, considering significant figures and rounding as needed.