A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being $\displaystyle 7$ cm and the height of the cone is equal to its diameter. Find the volume of the solid.

Radius of cone = radius of hemisphere \(\displaystyle =7 \mathrm{~cm}\) ∴ Height of cone \(\displaystyle =14 \mathrm{~cm}\) Volume of solid = Volume of hemisphere + volume of cone \[\begin{aligned} & =\frac{2}{3} \pi(7)^{3}+\frac{1}{3} \pi(7)^{2} 14 \\ & =\frac{1}{3} \times \frac{22}{7} \times 7 \times 7(14+14) \\ & =\frac{154}{3} \times 28=\frac{4312}{3} \mathrm{~cm}^{2} \text { or } 1437.33 \mathrm{~cm}^{2} \end{aligned} \]