If the total surface area of a solid hemisphere is 462 cm2,

As, the total surface area of the solid hemisphere $=462 \mathrm{~cm}^{2}$

$\Rightarrow 3 \pi r^{2}=462$

$\Rightarrow 3 \times \frac{22}{7} \times r^{2}=462$

$\Rightarrow r^{2}=\frac{462 \times 7}{3 \times 22}$

$\Rightarrow r^{2}=49$

$\Rightarrow r^{2}=\sqrt{49}$

$\Rightarrow r=7 \mathrm{~cm}$

Now, the volume of the solid hemisphere $=\frac{2}{3} \pi r^{3}$

$=\frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$

$=\frac{2156}{3} \mathrm{~cm}^{3}$

$=718 \frac{2}{3} \mathrm{~cm}^{3}$

$=718.67 \mathrm{~cm}^{3}$