Step 1 :The volume of a cylinder is given by the formula \(V = \pi r^2 h\), where \(r\) is the radius and \(h\) is the height.
Step 2 :In this case, the diameter is given as 8 inches, so the radius is half of that, or 4 inches.
Step 3 :The height is given as three times the radius, so the height is 12 inches.
Step 4 :We can substitute these values into the formula to find the volume.
Step 5 :Let \(r = 4\) and \(h = 12\).
Step 6 :Substitute \(r\) and \(h\) into the formula, we get \(V = 603.1857894892403\).
Step 7 :Rounding to the nearest hundredth, we get \(V = 603.19\).
Step 8 :Final Answer: The volume of the cylinder is approximately \(\boxed{603.19}\) cubic inches.