Final answer:
The volume of the silo can be found by calculating the volumes of the cylinder and hemisphere separately and then adding them. The volume of the cylinder is calculated using V = πr²h, and the volume of the hemisphere is calculated using V = (2/3)πr³. The radius of the silo is half of the diameter, which is 6m.
Step-by-step explanation:
The volume of the silo can be calculated by adding the volumes of the cylinder and the hemisphere. First, calculate the volume of the cylinder using the formula V = πr²h, where r is the radius and h is the height. Since the diameter is given as 12m, the radius is half of that, which is 6m. So the volume of the cylinder is V_cylinder = 3.142 × (6m)² × 41m = 4,722.408 m³.
Next, calculate the volume of the hemisphere using the formula V = (2/3)πr³, where r is the radius. The radius is the same as the radius of the cylinder, which is 6m. So the volume of the hemisphere is V_hemisphere = (2/3) × 3.142 × (6m)³ = 904.779 m³.
Finally, add the volumes of the cylinder and the hemisphere to get the total volume of the silo. V_silo = V_cylinder + V_hemisphere = 4,722.408 m³ + 904.779 m³ = 5,627.187 m³. Therefore, the volume of the silo is approximately 5,627.2 m³ (rounded to the nearest tenth).