Mathematics

Problem

A solid has square cross sections perpendicular to the x-axis taken over the interval

0\le x\le a

. At each

x

, the side length of the square is

s(x)=\sqrt{x}

. Which of the following expressions gives the volume

V(a)

of the solid as a function of

a

? a)

V(a)=\displaystyle \int_{0}^{a} x^{3/2}\,dx

V(a)=\displaystyle \int_{0}^{a} x\,dx

V(a)=\displaystyle \pi\int_{0}^{a} x\,dx

V(a)=\displaystyle \int_{0}^{a} \sqrt{x}\,dx