A solid has as its base the semicircular region defined by with

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

Problem

A solid has as its base the semicircular region defined by

x^2+y^2\le9

with

y\ge0

. Cross-sections perpendicular to the

y

-axis are equilateral triangles whose bases lie in the region. What is the volume of the solid? (a)

36\sqrt{3}

(b)

18\pi

(c)

18\sqrt{3}

(d)

9\sqrt{3}