The region between the curve and the line is the base of a solid

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

Problem

The region between the curve

y=x^{2}

and the line

y=4

is the base of a solid. Cross sections perpendicular to the

x

-axis are semicircles whose diameters lie in the region. What is the volume of the solid? (a)

\dfrac{128\pi}{15}

(b)

\dfrac{32\pi}{15}

(c)

\dfrac{64\pi}{15}

(d)

\dfrac{256\pi}{15}