A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being $\displaystyle 3.5$ cm and the total height of the solid is $\displaystyle 9.5$ cm. Find the volume of the solid.

Radius of hemisphere = Radius of cone \(\displaystyle =3 \cdot 5 \mathrm{~cm}=\frac{7}{2} \mathrm{~cm}\) Height of cone \(\displaystyle =9 \cdot 5-3 \cdot 5=6 \mathrm{~cm}\) Volume of solid = volume of hemisphere + volume of cone \[\begin{aligned} & =\frac{2}{3} \times \frac{22}{7} \times\left(\frac{7}{2}\right)^{3}+\frac{1}{3} \times \frac{22}{7} \times\left(\frac{7}{2}\right)^{2} \times 6 \\ & =\frac{77}{6} \times 13=\frac{1001}{6}=166.8 \mathrm{~cm}^{3} \end{aligned} \]