Anytime you deal with a composite shape, you should break it down into it's parts, and then find the volume of each part. Remember, the whole is just the sum of its parts.
The cone has a height of 10 and a diameter of 6. This means it has a radius of 3.
The volume of any cone is (1/3)πr2h. Therefore the volume of this cone would be (1/3)π(3)2(10) or 30π units3.
The hemisphere has a diameter of 6. This means it also has a radius of 3.
The volume of any sphere is (4/3)πr3. A hemisphere would be half that or (2/3)πr3. Therefore the volume of this hemisphere is (4/3)π(3)3 or 36π units3.
The total volume would be 30π + 36π or 66π units3. The decimal approximation is 207.35 units3.