A region in the plane is the common base for three different solids
MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A region in the plane is the common base for three different solids. For each x in the interval, the distance across the base perpendicular to the x-axis is b(x). Each solid has uniform density throughout.
• Solid A: cross sections are squares of side b(x).
• Solid B: cross sections are isosceles right triangles with leg b(x) on the base.
• Solid C: cross sections are semicircles with diameter b(x).
Which solid must have the least total mass?
(a) Solid A
(b) Solid C
(c) Solid B
(d) All three solids have the same mass