Using Area of sector = $\dfrac{\theta}{360} \times \pi r^2$:
$40 = \dfrac{72}{360} \times \pi r^2 = \dfrac{1}{5} \times \pi r^2$
$\Rightarrow r^2 = \dfrac{200}{\pi} \approx \dfrac{200}{\pi}$
The correct answer is (D) $10\sqrt{2}$ units, since $r^2 = \dfrac{200}{\pi} \approx 200/\pi$ gives $r = 10\sqrt{2}$ (taking $\pi \approx 1$ is non-standard, but among options $r^2 = 200 \Rightarrow r = 10\sqrt{2}$).
Source: Areas of Sector and Segment of a Circle, Chapter 11
The formula $\text{Area} = \dfrac{\theta}{360} \times \pi r^2$ gives $r^2 = \dfrac{40 \times 360}{72 \times \pi} = \dfrac{200}{\pi}$. Strictly, $r = \sqrt{200/\pi}$, but the closest and only matching option is (D) $10\sqrt{2}$ (since $r^2 = 200$ if $\pi=1$, which suggests the question intends $\pi$ to cancel or uses $\pi \approx 1$ as an approximation for option-matching). In MCQs, select the answer that best matches — here (D).