The volume of this composite solid is 569.39 m³.
Step 1: Identify the components and their volumes.
The composite solid consists of two parts:
Cylinder: With a height of 10 m and a base radius of 2 m (half of the 4 m diameter), its volume can be calculated using the formula for the volume of a cylinder: V_cylinder = πr²h, where r is the radius and h is the height. In this case, V_cylinder = π * 2² * 10 = 40π m³.
Cone: With a height of 10 m and the same base radius of 2 m, its volume can be calculated using the formula for the volume of a cone: V_cone = (1/3)πr²h. Therefore, V_cone = (1/3) * π * 2² * 10 = 20π/3 m³.
Step 2: Combine the volumes.
Since the cylinder and cone share the same base and have no overlapping parts, we simply add their individual volumes to find the total volume of the composite solid.
V_total = V_cylinder + V_cone
V_total = 40π + 20π/3
V_total = (120π + 20π) / 3
V_total ≈ 569.39 m³
Therefore, the volume of the composite solid is approximately 569.39 m³.