The region between the curves and for is the base of a solid

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

Problem

The region between the curves

x=y

and

x=2y

for

0\le y\le 3

is the base of a solid. Cross sections perpendicular to the

y

–axis are semicircles. Which definite integral represents the volume

V

of the solid? (a)

V=\displaystyle\int_{0}^{3}\frac{\pi}{2}y^{2}\,dy

(b)

V=\displaystyle\int_{0}^{3}\frac{\pi}{4}y^{2}\,dy

(c)

V=\displaystyle\int_{0}^{3}\frac{\pi}{8}y^{2}\,dy

(d)

V=\displaystyle\int_{0}^{3}\pi y^{2}\,dy