Answer
The radius increases by 7.70%.
Work Step by Step
$V_0 = 4\pi r_0^2$
After taking the balloon inside the house, the new volume $V$ is $1.160\times V_0$.
$V = 1.160\times V_0$
$4\pi r^2 = 1.160\times 4 \pi r_0^2$
$r^2 = 1.160 \times r_0^2$
$r = \sqrt{1.160 \times r_0^2}$
$r = 1.0770 ~r_0$
The radius increases by a factor of 1.0770 which is an increase of $0.0770 \times 100\%$ which is equal to 7.70%.
The radius increases by 7.70%.
