An ice cream cone is fully filled with ice cream in such a way that a scoop of ice cream forms a hemisphere above the cone. The height and the diameter of the cone are 11 cm and 7 cm respectively. How much ice cream is held by the ice cream cone?

The given situation can be represented by the following figure.

Diameter of the cone = 7 cm

Therefore, the radius of the cone $=\frac{7}{2} \mathrm{cm}$

Height of the cone = 11 cm

Radius of the hemisphere $=\frac{7}{2} cm$

Volume of the ice cream held by the cone = Volume of the cone + Volume of the hemisphere

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

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

$=\frac{1}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \left(11+2\times \frac{7}{2}\right)$

$=\frac{77}{6}\times 18$

$=231 {\mathrm{cm}}^3$

Thus, 231 cm³ of ice cream is held by the ice cream cone.