Elliptical Ice Cream

Geometry Level pending

Blackberry ice cream costs a dollar per cubic centimeter. You have a cone of it worth $402.62 that has an semi-ellipsoid on top while the cone shares the same cross-section of an ellipse. The cone is tightly packed with ice cream.

You know the height of the cone only is 9 cm. The height of the semi-ellipsoid is the same as the minor axis of the cross section. The major axis is \(\sqrt{2}\) times the minor axis. What is the measure of the semi-minor axis? Calculator required (sorry).

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