The base of a solid is the region enclosed by the graph of x^2 + 4y^2 = 4 and cross-sections perpendicular to the x-axis are squares. Find the volume of this solid.

Question

The base of a solid is the region enclosed by the graph of x^2 + 4y^2 = 4 and cross-sections perpendicular to the x-axis are squares. Find the volume of this solid. 
a. 8/3 
b. 8 pi/3 
c. 16/3 
d. 32/3 
e. 32 pi/3

Thanks in advance! :)

Damon · Answer

base is ellipse
integral of (2y)^2 dx from x = -2 to x = +2
whic is twice the integral from 0 to +2 of 4 y^2 dx
which is
twice integral from 0 to +2 of (4-x^2) dx
2 * [ 4 x -x^3/3] at x = 2
2 * [ 8 - 8/3)
2 * [16/3] = 32/3