The volume of the largest right circular cone that can be carved out from a cube of edge 4.2 cm is

1. 9.7 cm³

2. 77.6 cm³

3. 58.2 cm³

4. 19.4 cm³

Edge of cube = 4.2 cm

Radius of largest cone cut out (r) = $\dfrac{4.2}{2}$ = 2.1 cm

Height of largest cone cut out (h) = 4.2 cm.

Volume of cone (V) = $\dfrac{1}{3}πr^2h$

Putting values we get,

$V = \dfrac{1}{3} \times \dfrac{22}{7} \times (2.1)^2 \times 4.2 \\[1em] = \dfrac{22 \times 2.1 \times 2.1 \times 4.2}{3 \times 7} \\[1em] = \dfrac{407.484}{21} \\[1em] = 19.4 \text{ cm}^3$

Hence, Option 4 is the correct option.