A hemisphere is kept on top of a cube. Its front view is shown in the given figure. The total height of the figure is 21 cm. The ratio of curved surfaces area of hemisphere and total surface area of cube is 11 : 42. What is the total volume (in cm³) of figure?

$$\frac{{{\text{Curved surfaces area of hemisphere}}}}{{{\text{Total surface area of cube}}}} = \frac{{2\pi {r^2}}}{{6{a^2}}}$$

3r = 21
r = 7 cm
Total volume of figure = Volume of hemisphere + Volume of cube
= $$\frac{2}{3}$$πr³ + a³
= $$\frac{2}{3}$$ × $$\frac{{22}}{7}$$ × 7 × 7 × 7 + 14³
= 718.66 + 2744
= 3462.67 cm³