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