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

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

Problem

A solid has rectangular cross-sections perpendicular to the x-axis. For each cross section, the height is

k

times its base. The base region is bounded by the graph of

y = 4 - x^{2}

and the x-axis for

-2 \le x \le 2

. If the volume of the solid is

120

cubic units, determine the value of

k

. Express your answer to the nearest hundredth.