A storage vessel is a cylinder of radius 2.1 m and height 12 m, closed at the bottom by a cone of the same radius hanging 5 m below it. Find the capacity of the vessel in cubic metres. (Take π = 22/7.)

Base area $\pi r^2=\frac{22}{7}(4.41)=13.86m^2$. Cylinder = $13.86\times 12=166.32{\text{m}}^3$. Conical bottom = $\frac{1}{3}(13.86)(5)=23.1m^3$. Because the cone hangs BELOW the cylinder it adds space, so capacity $=166.32+23.1=189.42{\text{m}}^3$. 235.62 drops the $\frac{1}{3}$; 143.22 subtracts the cone, which would be right only if the cone bulged upward into the vessel; 166.32 ignores the cone.