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Putting a Sphere into A Cubical Box

Consider this photo:


It is a picture of the Hayden Planetarium, which is part of the American Museum of Natural History in New York. In addition to offering astronomical exhibits and sky shows, it offers a chance to do some mathematics. For example, the sphere, 87 feet in diameter, is enclosed inside a cube...assume each face of the glass cube touches the sphere at a single point.

Task: What fraction of the volume of the sphere is the cubical building housing the sphere?

Task 2: The glass cube is covered by large rectangular panes of glass. Are these panes golden rectangles? (Explain)