MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
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