Final answer:
The volume of the cylinder is an irrational number because it includes π. The radius and height of the cylinder are rational numbers. Therefore, statements A is true, and statements B, C, and D are false.
Step-by-step explanation:
The question pertains to volume calculation and number properties, specifically rational and irrational numbers, using a given cylinder with radius 17 inches and height 14.6 inches. To determine the volume of this cylinder, we use the formula V = πr²h. Upon calculating the volume with these dimensions, we get V = π(17 inches)²(14.6 inches), a number which will include π. Since π is an irrational number, the product will also be irrational, making statement A correct. For statement B, it's crucial to clarify that not all square roots are rational; a number is rational if it can be expressed as a ratio of two integers. The radius is given as 17 inches, a rational number, but this information is not related to whether square roots are rational or not, thus statement B is incorrect. Statement C is incorrect for the same reason A is correct: the volume contains π, making it irrational. The height of the cylinder is given as 14.6 inches, a number that can be expressed as a fraction (146/10), making it a rational number and rendering statement D false.