OG详解-OG5 数学1 Q15

Choice C is correct. The volume, V, of a right circular cylinder is given by the formula V= πr² h, where r is the radius of the base of the cylinder and h is the height of the cylinder. It’s given that a right circular cylinder has a height of 6 centimeters. Therefore, h = 6. It’s also given that the cylinder has a base diameter of 22 centimeters. The radius of a circle is half the diameter of the circle. Since the base of a right circular cylinder is a circle, it follows that the radius of the base of the right circular cylinder is22​2​, or 11, centimeters. Therefore, r = 11. Substituting 11 for r and 6 for h in the formula V= πr² h yields V= π (11)² (6), which is equivalent to V= π (121)(6), or V= 726π. Therefore, the volume, in cubic centimeters, of the cylinder is 726π.
Choice A is incorrect. This is the volume of a right circular cylinder that has a base diameter of 2√2​2, not 22, centimeters and a height of 6 centimeters. Choice B is incorrect. This is the volume of a right circular cylinder that has a base diameter of 4√11​, not 22, centimeters and a height of 6 centimeters. Choice D is incorrect. This is the volume of a right circular cylinder that has a base diameter of 44, not 22, centimeters and a height of 6 centimeters.