Let be the region bounded by and on

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

Problem

Let

R

be the region bounded by

y=0

and

y=4-x^{2}

0\le x\le 2

. Rectangular cross sections are taken perpendicular to the

x

–axis; the height of each rectangle is

p

times its base (the base is the vertical segment from

y=0

y=4-x^{2}

). If the volume of the solid formed in this way is

40

cubic units, what is the value of

p

? (a)

\dfrac{15}{2}

(b)

\dfrac{75}{32}

(c)

\dfrac{75}{64}

(d)

\dfrac{25}{24}