Turn the graph of $y=\frac{1}{x}$ by $45^{\circ}$ counter-clockwise and consider the bowl-like top part of the curve (the part above $y=0$). We let a $2D$ fluid accumulate in this $2D$ bowl until the maximum depth of the fluid is $\frac{2\sqrt{2}}{3}$. What’s the area of the fluid used?