Mathematics

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}

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

\dfrac{81}{10}

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