The region in the first quadrant bounded by the y-axis and the curve for is the…
MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The region in the first quadrant bounded by the y-axis and the curve x=y2 for 0≤y≤1 is the common base of two solids, with cross-sections taken perpendicular to the y-axis.
• Solid U has square cross-sections.
• Solid V has rectangular cross-sections whose base equals that of the square and whose height is ky, where k is a positive constant.
For what value of k do the two solids have equal volumes?
(a) 1
(b) 54
(c) 45
(d) 53