Consider the half-ellipsoid shown below whose equation is given by Note that x, y and z are in meters. ??????? We want to build a rectangular box inside the ellipsoid: the bottom lies on the XY plane, the sides of the box are parallel to the axes, the top vertices are located on the ellipsoid. Determine the maximum volume of such a box. Set u solutionspile.com

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Consider the half-ellipsoid shown below whose equation is given by

$\frac{x^{2}}{25}+\frac{y^{2}}{9}+\frac{z^{2}}{4}=1$

Note that x, y and z are in meters.

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We want to build a rectangular box inside the ellipsoid: the bottom lies on the XY plane, the sides of the box are parallel to the axes, the top vertices are located on the ellipsoid. Determine the maximum volume of such a box.

Set up an integral that gives the volume of the solid bounded by the plane z = 0 and the half-ellipsoid, evaluate the integral with Nspire and round it to the nearest hundredth. Explain clearly how the integration bounds were determined, using one or more figures.

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