In the equation above S = 4πr², if the value of r is doubled, then the corresponding value of S is multiplied by

This choice suggests that doubling the radius would reduce the surface area to a quarter of its original value. However, this is incorrect because increasing \( r \) actually increases \( S \), not decreases it. The relationship between \( S \) and \( r \) is quadratic, leading to an increase rather than a decrease.

This option implies that doubling the radius results in the surface area being half of its original size. This is also inaccurate; the surface area increases as the radius increases, and it does not decrease to half. The quadratic relationship ensures that \( S \) grows, not shrinks.

Choosing 2 suggests that the surface area doubles when the radius is doubled. While \( S \) does increase, it actually quadruples due to the squaring effect of the radius in the equation. Thus, this option misrepresents the relationship between \( S \) and \( r \).

This option indicates that the surface area is increased eightfold when the radius is doubled. However, this is incorrect, as the increase is only by a factor of 4, stemming from the square of the radius change, not a cubic relationship.