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.

Diameter of hemispherical bowl = 7.2 cm

Radius of hemispherical bowl (r) = 3.6 cm

Volume of hemispherical bowl = $\dfrac{2}{3}πr^3$.

Radius of cone (R) = 4.8 cm.

Let height of cone = h cm.

Volume of cone = $\dfrac{1}{3}πR^2h$.

Volume of cone = Volume of hemispherical bowl.

$\therefore \dfrac{1}{3}π \times (4.8)^2 \times h = \dfrac{2}{3} \times π \times (3.6)^3 \\[1em] \Rightarrow h = \dfrac{2π \times 46.656 \times 3}{3 \times π \times 23.04} \\[1em] \Rightarrow h = \dfrac{93.312}{23.04} \\[1em] \Rightarrow h = 4.05 \text{ cm}.$

Hence, the height of the cone is 4.05 cm.