(d) $\dfrac{2\pi}{3}$ cu cm
For a cube of edge 2 cm, the largest cone has radius $r = 1$ cm and height $h = 2$ cm.
$$V = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (1)^2(2) = \frac{2\pi}{3} \text{ cu cm}$$
The largest cone carved from a cube of edge $a$ has its base circle fitting the face of the cube, so radius $r = a/2$, and height = edge = $a$. Here $a = 2$ cm, giving $r = 1$ cm, $h = 2$ cm. Apply the cone volume formula directly. A common mistake is taking $r = 2$ cm (the full edge) instead of half the edge.