Let be the region in the first quadrant bounded by and

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

Problem

Let

R

be the region in the first quadrant bounded by

x=y

and

x=y^{2}

. A solid has base

R

, and cross sections perpendicular to the

y

-axis are right isosceles triangles whose hypotenuse lies in

R

. What is the volume of the solid? (a)

\dfrac{1}{60}

(b)

\dfrac{1}{30}

(c)

\dfrac{1}{120}

(d)

\dfrac{\sqrt{3}}{120}