Final answer:
Possible dimensions of a cylinder with a surface area of 1 m² can vary; the radius and height must balance to achieve the surface area. The surface area includes areas of two bases and the side of the cylinder. Different combinations of the radius and height are possible as long as the total area remains 1 m².
Step-by-step explanation:
The question asks us to determine possible dimensions of a cylinder with a known surface area of 1 meter squared. The surface area of a cylinder is composed of two parts: the areas of the two circular bases and the area of the side, which can be seen as a rectangle if unwrapped. The formula for the surface area (A) of a cylinder can be written as:
A = 2πr² + 2πrh
where r is the radius, h is the height, and π (pi) approximates to 3.1415927. Because the exact values are not given, we can only suggest that there are multiple combinations of r and h that could give a surface area of 1 m². For instance, a cylinder with a tiny radius would need a much greater height to have a surface area of 1 m² compared to a cylinder with a larger radius.
If we take a hypothetical example and start with a radius (r) of 0.1 m, we can substitute this into the surface area formula and solve for the height. Remembering to maintain a balance between the area of the bases and the side, some trial and error will be required to find a height that gives a total surface area of 1 m².