Mathematics

Problem

Consider a solid whose base lies in the region bounded by the graphs of

y=\sqrt{x}

and the

x

-axis for

0\le x\le 9

. Cross sections taken perpendicular to the

x

-axis are semicircles whose diameters extend from the

x

-axis up to the curve. Which of the following expressions gives the area

A(x)

of a representative cross section at position

x

, written solely in terms of

x

? a)

A(x)=\dfrac{\pi x}{4}

A(x)=\dfrac{\pi x}{8}

A(x)=\dfrac{\pi}{2}x

A(x)=\dfrac{\pi}{8}\sqrt{x}