Let be the region bounded by the graph of and the –axis

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

Problem

Let

R

be the region bounded by the graph of

y=3x-x^{2}

and the

x

–axis. Cross sections of the solid with base

R

, taken perpendicular to the

x

–axis, are equilateral triangles. What is the exact volume of the solid? (a)

\dfrac{27\sqrt{3}}{10}

(b)

\dfrac{81\sqrt{3}}{40}

(c)

\dfrac{81}{10}

(d)

\dfrac{81\sqrt{3}}{20}