Final answer:
The radius that maximizes the volume of an open-top cylinder made from 18 square inches of material, without using calculus, is most likely 3 inches based on logical reasoning around the fixed surface area constraint.
Step-by-step explanation:
To maximize the volume of an open-top cylinder using a fixed amount of material, one must understand that the surface area is used for the sides and the bottom of the cylinder, with no top. The total material available is 18 square inches which can be represented as the sum of the area of the base (circle) and the lateral surface area (rectangle). This gives us the equation 18 = πr² + 2πrh. To find the maximum volume, we would need to optimize this equation which is a calculus problem involving derivatives. However, to answer this question, we can solve it logically by considering that when r = h, the cylinder's volume will be maximized due to the nature of the formula for volume V = πr²h favoring a balance between the radius and height for a fixed surface area.
Without using calculus, the closest choice for the radius that could maximize the volume is 3 inches, as the other options will not allow both terms (base and lateral surface area) to be covered within the 18 square inches limit. Hence, the answer would be a) 3 inches.