Answer
The radius increases by a factor of 1.4
Work Step by Step
$A_0=4\pi r_0^2$
After the balloon expands, the new surface area A is $2.0 \times A_0$.
$A = 2.0 \times A_0$
$4 \pi r^2 = 2.0 \times 4 \pi r_0^2$
$r^2 = 2.0 \times r_0^2$
$r = \sqrt{2.0 \times r_0^2}$
$r = 1.4 \times r_0$
The radius increases by a factor of 1.4
