Question

The base of the solid is in the region between the x-axis and the parabola y=4-x^2. The cross sections of the solid Perpendicular to the y-axis are semicircles. Compute the volume of the solid.

Answer 1

I realize I am Integrating with respect to y since the semicircles are perpendicular to the y-axis. I found the intersection points to be from -2 to 2. Those are also the limits of integration.

I am having trouble setting up the integral however.

Answer 2

I also know that the area of a semicircle is:\[\frac{ \pi r^2 }{ 2 }\]

Answer 3

@campbell_st @Hero @AravindG @Agent_Sniffles

Answer 4

@precal

Answer 5

I think if you draw it, it helps but this is not my strong point

Answer 6

Ohh I forgot to mention since I am integrating with respect to y the limits of integration are from 0 to 4 sorry.

Answer 7

still not my strong point

Answer 8

Thanks anyways :) .