The volume of a cylinder is given by the product of the area of its base and its height. The base of a cylinder is a disk which means that its area is given by:
![A=\pi r^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/lcgfavc89jro4qntamn2b9gfliomu1jwuf.png)
Where r is the radius of the base. Here we have the diameter of the base which is two times its radius. Then the radius of the base is:
![r=(6)/(2)=3](https://img.qammunity.org/2023/formulas/mathematics/college/741a9yo7djl09dkvx9trag97agoo5yu9os.png)
Then the area of the base is:
![A=\pi\cdot3^2=9\pi\approx9\cdot3=27](https://img.qammunity.org/2023/formulas/mathematics/college/7qxqh9pblkbqciunnibmlunfvhkcx4wcph.png)
Now that we have the area of the base we just need to multiply it by the height:
![V=27\cdot8=216](https://img.qammunity.org/2023/formulas/mathematics/college/2oxwv4128qh7yn2e1dwgqo5n56l7xgrhaq.png)
Then the answer is 216 in³.