Mensuration (Pyramid, Cones and Spheres) - Volume and Surface Area of Composite Solids

A solid consists of a triangular prism above a rectangular-based pyramid. They share a horizontal rectangular face measuring \(18\text{ cm}\) by \(10\text{ cm}\).
The prism has length \(18\text{ cm}\). Its triangular cross-section has base \(10\text{ cm}\) and perpendicular height \(6\text{ cm}\). The total vertical height of the solid is \(15\text{ cm}\).

1. Find the volume of the solid.

   [3]

2. A designer increases the perpendicular height of the prism’s triangular cross-section from \(6\text{ cm}\) to \(8\text{ cm}\). The shared rectangular face and total vertical height remain unchanged.

   The designer claims, “The total volume stays the same because one part becomes taller by the same amount that the other becomes shorter.”

   Determine whether the claim is correct. Calculate the change in total volume and explain your conclusion.

   [3]