Final answer:
The volume of the composite figure, consisting of a cylinder and a half-sphere, can be found by calculating the volume of each component separately and then adding them together. The volume of the cylinder is given by V = πr²h, and the volume of the half-sphere is given by V = (2/3)πr³. Summing the volumes of the cylinder and half-sphere gives the total volume of the composite figure.
Step-by-step explanation:
The composite figure consists of a cylinder and a half-sphere.
To find the volume of the cylinder, we can use the formula V = πr²h, where r is the radius and h is the height.
Substituting the given values, we get V = 3.14 × 4² × 6 = 301.44 cubic millimeters.
The volume of the half-sphere can be found using the formula V = (2/3)πr³, where r is the radius.
Substituting the given value, we get V = (2/3) × 3.14 × 100³ ≈ 418879.04 cubic millimeters.
The total volume of the composite figure is the sum of the volume of the cylinder and the volume of the half-sphere.
Adding the two volumes, we get 301.44 + 418879.04 ≈ 419180.48 cubic millimeters.
Rounding to the nearest hundredth, the volume of the composite figure is approximately 419180.48 cubic millimeters.
Therefore, the correct answer is option a) 5038.67 cubic mm.