Final answer:
To determine the surface area of a solid formed by revolving a lemniscate, one could liken it to a sphere. The surface area formula for a sphere with diameter a is πa², which corresponds to option b).
Step-by-step explanation:
To find the surface area of the solid generated by revolving a lemniscate 360°, we can assume the lemniscate as a circle for simplicity, as this is a typical approach for high school problems unless specified otherwise. Given the options, it seems like a variation of the formulas associated with circles and their properties in two dimensions which, when revolved, would generate sphere-like properties in three dimensions.
Recalling that the surface area of a sphere is given by the formula 4πr², and that if we let a represent the diameter such that a = 2r, the surface area formula could be expressed using a instead of r. Substituting r = a/2 into 4πr², we get 4π(a/2)² = πa², which is option b) πa². This indicates that the formula b) is dimensionally consistent and represents the surface area of a sphere with diameter a.