Fermentation tanks are designed in the form of cylinder mounted on a cone as shown below : The total height of the tank is $\displaystyle 3.3$ m and height of conical part is $\displaystyle 1.2$ m. The diameter of the cylindrical as well as conical part is $\displaystyle 1$ m . Find the capacity of the tank. If the level of liquid in the tank is $\displaystyle 0.7$ m from the top, find the surface area of the tank in contact with liquid.

Diameter = $\displaystyle 1$ m \[\mathrm{r}=0.5 \mathrm{~m} \] Height of Cylinder \(\displaystyle (\mathrm{H})=3.3-1.2=2.1 \mathrm{~m}\) Capacity of the tank = Volume of cylinder + Volume of cone \[\begin{aligned} & =\frac{22}{7} \times(0.5)^{2} \times 2.1+\frac{1}{3} \times \frac{22}{7} \times(0.5)^{2} \times 1.2 \\ & =1.96 \mathrm{~m}^{3} \end{aligned} \] Slant height \(\displaystyle (l)=\sqrt{(1.2)^{2}+(0.5)^{2}}=1.3 \mathrm{~m}\) Height of cylindrical part in contact with liquid \(\displaystyle =2.1-0.7=1.4 \mathrm{~m}\) Surface area of tank in contact with liquid = Curved Surface Area of Cylindrical part in contact with liquid + Curved surface Area of cone \[\begin{aligned} & =2 \times \frac{22}{7} \times 0.5 \times 1.4+\frac{22}{7} \times 0.5 \times 1.3 \\ & =6.44 \mathrm{~m}^{2} \text { (approx.) } \end{aligned} \]