A hemisphere is kept on a cube of side 14 cm. The surface of the hemisphere fits perfectly over the cube's top face. Then find the total volume of the figure?

3,462.66 cm³

since the surface of the hemisphere fits perfectly over the cube;

diameter of hemisphere = side of cube

⇒ = 14 cm

⇒ volume of their figure = \(\frac{2}{3}\) \(\pi \)r³ + (side)³

= \(\frac{2}{3}\) × \(\frac{22}{7}\) × (7)³ + (14)³

= 718.66 + 2,744 = 3,462.66 cm³