Final answer:
To find the radius and height of the box with the largest possible volume, calculate the length of the ribbon required, which can be done using the circumference formula. Use the volume formula to find the maximum volume of the box. There is no maximum height, so none of the options provided are correct.
Step-by-step explanation:
To find the radius and height of the box with the largest possible volume, we can start by determining the length of the ribbon required to go around the box. This can be calculated by using the circumference formula: C = 2πr, where C is the length of the ribbon and r is the radius of the box.
In this case, 25cm of the ribbon is required for the bow, so the remaining ribbon length that goes around the box is 265cm - 25cm = 240cm.
Since the ribbon goes around the box once and the box is cylindrical, its circumference is equal to the length of ribbon needed. Therefore, 2πr = 240cm.
Simplifying the equation, we have 2πr = 240cm, which means r = 240cm / (2π) ≈ 38.191cm (rounded to three decimal places).
Now that we have the radius, we can calculate the height of the box by using the volume formula: V = πr²h.
Given that the volume of the box should be maximized, the height should be as large as possible. However, there is no information given that would indicate a restriction on the height. Therefore, there is no maximum height, and any value can be chosen. The answer choices provided do not reflect this, so none of the given options are correct.