For the region bounded by the curve

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

Problem

x = 3y^{2}

, the

y

-axis, and the horizontal lines

y=0

and

y=2

, a solid is generated by revolving the region about the

y

-axis. What is the radius, expressed as a function of

y

, of a representative cross-section perpendicular to the axis of rotation? (a)

r(y)=y

(b)

r(y)=\sqrt{3}\,y

(c)

r(y)=3y^{2}

(d)

r(y)=3y