For , the region under and above the -axis is the common base of two solids. • Solid…

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

For

0 \leq x \leq \frac{\pi}{2}

, the region under

y = \cos x

and above the

x

-axis is the common base of two solids. • Solid P has cross-sections perpendicular to the

x

-axis that are squares. • Solid Q has cross-sections perpendicular to the

x

-axis that are rectangles whose height is three times their width. What is

V_{Q} - V_{P}

, the difference between the volumes of the two solids? (a)

\pi

(b)

\frac{\pi}{4}

(c)

\frac{\pi}{2}

(d)

\frac{3\pi}{4}