Answer
The new area is twice the size of the original area. Since we solved the question algebraically, we can see that this result holds in general.
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 angle be $\theta_1$ and let the original radius be $r_1$:
$A_1 = \frac{\theta_1 ~r_1^2}{2}$
We can find an expression for the new area:
$A_2 = \frac{\theta_2 ~r_2^2}{2}$
$A_2 = \frac{(\theta_1/2) ~(2r_1)^2}{2}$
$A_2 = 2\times \frac{\theta_1 ~r_1^2}{2}$
$A_2 = 2~A_1$
The new area is twice the size of the original area. Since we solved the question algebraically, we can see that this result holds in general.
