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Problem 3. Show that the volume of the largest parallelpiped (i.e., rectangular prism with sides parallel to the coordinate axes) that can be inscribed in the ellipsoid 28 x2 + y² z² + = 1 a² 62 c2 is 8abc/3√3. Hint: Let (x, y, z) be one of the corners of an inscribed parallelpiped. Can you express its volume in terms of x, y, and z?

Problem 3. Show that the volume of the largest parallelpiped (i.e., rectangular prism with sides parallel to the coordinate axes) that can be inscribed in the ellipsoid 28 x2 + y² z² + = 1 a² 62 c2 is 8abc/3√3. Hint: Let (x, y, z) be one of the corners of an inscribed parallelpiped. Can you express its volume in terms of x, y, and z?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.1: Prisms, Area And Volume
Problem 30E: A storage shed is in the shape of a trapezoidal prism. Each trapezoid represents one of its bases....
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Problem 3. Show that the volume of the largest parallelpiped (i.e., rectangular prism with sides parallel to the coordinate axes) that can be inscribed in the ellipsoid 28 x2 + y² z² + = 1 a² 62 c2 is 8abc/3√3. Hint: Let (x, y, z) be one of the corners of an inscribed parallelpiped. Can you express its volume in terms of x, y, and z?
Transcribed Image Text:Problem 3. Show that the volume of the largest parallelpiped (i.e., rectangular prism with sides parallel to the coordinate axes) that can be inscribed in the ellipsoid 28 x2 + y² z² + = 1 a² 62 c2 is 8abc/3√3. Hint: Let (x, y, z) be one of the corners of an inscribed parallelpiped. Can you express its volume in terms of x, y, and z?
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