A solid has base the disk (x^ 2 +y^ 2 9 ) in the (xy )-plane

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

Problem

A solid has base the disk

x^{2}+y^{2}\le 9

in the

xy

-plane. For each

x

in the interval

-3\le x\le 3

, the cross section perpendicular to the

x

-axis is a rectangle whose width equals the full vertical length of the base at that

x

and whose height is

5-x^{2}

. Determine the volume of the solid.