A solid has the shape of a cone surmounted by a hemisphere, each with a radius of 3.5 cm and a total height of 9.5 cm. Determine the volume of the solid.

The given figure is a combination of cone and hemisphere.

Radius of the cone (r) = 3.5 cm

Height of the cone (h) = 6 cm

Radius of the hemisphere (R) = 3.5 cm

Therefore, the volume of the solid

$=$ Volume of the cone + Volume of the hemisphere

$=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h} + \frac{2}{3}{\mathrm{\pi R}}^3$

$=\frac{1}{3}\mathrm{\pi }\times {(3.5)}^2\times 6+\frac{2}{3}\mathrm{\pi }\times {(3.5)}^3$

$=\frac{1}{3}\times \frac{22}{7}\times {(3.5)}^2\left(13\right)$

$=166.83 {\text{cm}}^3$