Let be the region bounded by ,

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

Problem

Let

R

be the region bounded by

x=0

x=y^{2}

, and

0\le y\le 3

. A solid is formed whose cross sections perpendicular to the

y

-axis are rectangles with height equal to five times their base width. Determine the volume of this solid.