# Math Help - volume

1. ## volume

Find the volume of the solid whose base is the region between the x-axis and the inverted parabola f(x)=4-x^2 if every vertical cross sections of the solid perpendicular to the y-axis are semicircles.

2. Originally Posted by mikegar813
Find the volume of the solid whose base is the region between the x-axis and the inverted parabola f(x)=4-x^2 if every vertical cross sections of the solid perpendicular to the y-axis are semicircles.
$V = \int_c^d A(y) \, dy$

$y = 4-x^2$

$x = \sqrt{4-y}$

radius of each semicircular cross section is $x$

$A = \frac{\pi}{2} x^2 = \frac{\pi}{2}(\sqrt{4-y})^2 =$

$V = \frac{\pi}{2}\int_0^4 4-y \, dy$