Mathematics

Problem

Let

S

be the solid whose base is the region bounded by

y=\sqrt{x}

and

y=\dfrac{x}{4}

for

0\le x\le 4

. A cross section perpendicular to the

x

-axis at position

x

is a triangle whose height is three times its base, where the base equals the distance between the two curves at that

x

-value. What is the volume of

S

? a)

\dfrac{44}{5}

\dfrac{22}{5}

5

\dfrac{22}{15}