Answer
The new area is four times the size of the original area.
Work Step by Step
Let $\theta$ be the angle in radians. Let $A$ be the area of the sector. Then the ratio of the angle $\theta$ to $2\pi$ is equal to the ratio of the sector area to the area of the whole circle.
$\frac{\theta}{2\pi} = \frac{A}{\pi ~r^2}$
$A = \frac{\theta ~r^2}{2}$
Let the original radius be $r_1$:
$A_1 = \frac{\theta ~r_1^2}{2}$
We can find an expression for the new area when the radius is doubled:
$A_2 = \frac{\theta ~r_2^2}{2}$
$A_2 = \frac{(\theta) ~(2r_1)^2}{2}$
$A_2 = 4\times \frac{\theta ~r_1^2}{2}$
$A_2 = 4~A_1$
The new area is four times the size of the original area.
