If you double the radius of a sphere does its surface area also double?

No, if you double the radius of a sphere, its surface area does not double; it actually increases by a factor of four. The surface area ( A ) of a sphere is given by the formula ( A = 4\pi r^2 ). When the radius ( r ) is doubled, the new surface area becomes ( A' = 4\pi (2r)^2 = 4\pi (4r^2) = 16\pi r^2 ), which is four times the original surface area.