31.

A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.

Given, radius of cone = 4.8 cm

Volume of hemispherical bowl = $\frac{2}{3}{\mathrm{\pi r}}^3$

                                           = $\frac{2}{3}\mathrm{\pi }(3.6{)}^3 {\mathrm{cm}}^3$

Volume of cone = $\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

                       = $\frac{1}{3}\mathrm{\pi } \times (4.8{)}^2 \times \mathrm{h}$

But, Volume of bowl = Volume of cone

$\Rightarrow$$\frac{2}{3}\mathrm{\pi }(3.6{)}^3 {\mathrm{cm}}^3$ = $\frac{1}{3}\mathrm{\pi } \times (4.8{)}^2 \times \mathrm{h}$

$\Rightarrow \mathrm{h} = \frac{2 \times 3.6 \times 3.6 \times 3.6}{4.8 \times 4.8} = 4.05 \mathrm{cm}$

Thus, the height of the cone is 4.05 cm.