Final answer:
The volume of the structure is calculated by finding the volume of the cylinder (V = πr²h) and the hemisphere (V = (2/3)πr³) separately and adding them together. However, the given options do not match the calculated volume, suggesting a possible error in the options provided or the calculations.
Step-by-step explanation:
To find the volume of the structure composed of a cylinder with a hemisphere on top, we need to calculate the volume of each part separately and then add them together. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height of the cylinder.
The given radius is 5m and the height is 8m for the cylinder. Hence, the volume of the cylinder is:
Vcylinder = π × (5m)² × 8m = π × 25m² × 8m = 200π m³
The volume of a hemisphere is half the volume of a sphere, which can be calculated using the formula V = (2/3)πr³. Since we only need the volume of the hemisphere, we have:
Vhemisphere = ½ × (4/3)π × (5m)³ = ½ × (4/3)π × 125m³ = (2/3)π × 125m³ = (250/3)π m³
Now, adding both volumes together:
Vtotal = Vcylinder + Vhemisphere = 200π m³ + (250/3)π m³
The final volume is approximately:
Vtotal = 200π + × (250/3)π = π (600 + 250/3) = (1750/3)π m³ ≈ 1832.5π m³ ≈ 5,758.48 m³
However, the current options provided are not matching the calculated volume, so there might be something incorrect with the given options or the calculation. We have to ensure that the formulas and calculations are correct and check whether the provided options need revising.