Mathematics

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

\frac{\pi}{4}

\frac{\pi}{2}

\frac{3\pi}{4}