Three solids, each with the same two–dimensional base region in the xy-plane, are formed by perpendicular cross sections whose widths across the base are denoted w(x).
• Solid P has square cross sections of side length w(x).
• Solid Q has equilateral-triangle cross sections whose side length is w(x).
• Solid R has semicircular cross sections whose diameter is w(x).
Which solid necessarily has the greatest volume?
a) Solid Q
b) Solid R
c) Solid P
d) The volumes of all three solids are equal