Estimating a capped festival column

Core stretch

A solid festival column is modelled as a 4.2 m cylinder with a 0.6 m conical cap. Circumferences measured at three sections are 2.10 m, 2.20 m and 2.15 m. Use \(\pi=3.142\) and the mean circumference.

1. Show that the estimated cross-sectional area is \(0.368\text{ m}^2\) to 3 s.f.[2]
2. Find the solid volume to 3 d.p.[2]
3. Find total exterior area, including the one circular end, to 2 d.p.[2]
4. The casting density is \(700\text{ kg/m}^3\). A hoist rated at 28 tonnes moves 120 columns. Find the minimum number of lifts and state an assumption.[2]