Let be the solid whose base is the region bounded by the curve and the –axis for

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

Problem

Let

S

be the solid whose base is the region bounded by the curve

y=\sqrt{x}

and the

x

–axis for

0\le x\le 4

. Squares are erected perpendicular to the

x

–axis, and the side length of each square is

k\sqrt{x}

, where

k>0

. For what value of

k

is the volume of

S

equal to

20

cubic units? (a)

\sqrt{\dfrac{5}{4}}

(b)

\sqrt{\dfrac{5}{2}}

(c)

\sqrt{\dfrac{2}{5}}

(d)

\sqrt{\dfrac{4}{5}}