APFIVE Volume with Circular Cross Sections
The region enclosed by the graphs of $$ y = \sqrt{x} $$ and $$ y = \frac{x}{4} $$ is the base of a solid. For the solid, each cross section perpendicular to the y-axis is a circle whose diameter equals the width of the region at that y-value. Which of the following expressions gives the volume of the solid?
A
$$ \frac{\pi}{4} \int_0^{16} (\sqrt{x} - \frac{x}{4})^2 \, dx $$
B
$$ \frac{\pi}{4} \int_0^4 (4y - y^2)^2 \, dy $$
C
$$ \pi \int_0^4 (4y - y^2)^2 \, dy $$
D
$$ \frac{\pi}{2} \int_0^4 (4y - y^2) \, dy $$
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