A solid has square cross-sections perpendicular to the x-axis

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

Problem

A solid has square cross-sections perpendicular to the x-axis. The base region is bounded above by

y = x

and below by

y = kx^{2}

on the interval

0 \le x \le 1

. The volume of the solid is

\dfrac{1}{30}

cubic unit. Determine the value of the constant

k