Calculus

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! :)

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  1. 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

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