Thread: Volume of bounded region

Let R denote the region enclosed by the y-axis, the line y = 1, and the curve
y = sqrt(x). Compute the volume of the solid whose base is R and whose cross sections perpendicular to the y-axis are semicircles.

I don't get it.. i did integral(pi*(y^2)^2)dy) from y=0 to y=1. i got pi/10
The answer is supposed to be pi/40.

Originally Posted by bfpri

Let R denote the region enclosed by the y-axis, the line y = 1, and the curve
y = sqrt(x). Compute the volume of the solid whose base is R and whose cross sections perpendicular to the y-axis are semicircles.

I don't get it.. i did integral(pi*(y^2)^2)dy) from y=0 to y=1. i got pi/10
The answer is supposed to be pi/40.

Hi bfpri,





and all of these semicircles have diameter x, therefore radius (0.5)x.
Their areas are half the area of a circle of the same radius.
Therefore,

thanks!