The region bounded by the -axis and the curve on is revolved about the horizontal line

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

Problem

The region bounded by the

x

-axis and the curve

y = 4 - x^{2}

-2 \le x \le 2

is revolved about the horizontal line

y = k

, where

0 \le k \le 4

. Derive a single integral in terms of

k

that represents the volume of the resulting solid.