Consider the region in the first quadrant bounded on the right by and on the left by…

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

Problem

Consider the region in the first quadrant bounded on the right by

x=y^{2}

and on the left by the

y

-axis for

0\le y\le 2

. A solid is formed whose cross sections perpendicular to the

y

-axis are triangles whose height is exactly twice their base, with the base lying in the region. Determine the exact volume of this solid.