As viewed from above, a swimming pool has the shape of the ellipse
x^2/25 +y^2/16=1
The cross sections perpendicular to the ground and parallel to the y-axis are squares.
Find the total volume of the pool. (Assume the units of length and area are meters
and square meters respectively.)
So for a given y, the two x values are and the length of that segment is . Since "cross sections perpendicular to the ground and parallel to the y-axis are squares", the depth at that y is also and so the cross section area is the square of that, . Taking the thickness of an "infinitesmal slab" to be [itex]dy[/tex], the volume of such a slab is [itex]\frac{25}{4}(16- y^2)dy[/itex] and the total volume is the integral of that.