Sec 2 E Math Mock Paper 2-Q08 - Frustum display-plinth modelling

A decorative display is formed from a frustum of base radius 12 cm by removing a similar cone of radius 6 cm. The frustum height is 36 cm and the removed cone height is \(h\).

1. Show that \(h=36\).
2. Find the frustum volume. The frustum is fixed to a solid cuboid plinth \(36\times26\times6\) cm. The display is moulded from resin of density \(0.8\text{ g/cm}^3\); resin costs $2.40/kg, and exterior sealant costs $0.40 per \(100\text{ cm}^2\), including the bottom.
3. Suggest and justify a sensible selling price.