A region in the plane serves as the common base for two solids

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A region

R

in the plane serves as the common base for two solids. • Solid

P

has square cross sections perpendicular to the

y

-axis and is made of material with constant density

\rho

. • Solid

Q

has semicircular cross sections perpendicular to the

y

-axis whose diameters lie in

R

and is made of material with constant density

2\rho

. Without setting up or evaluating any integrals, decide which solid has the greater mass and support your conclusion concisely.