In the opening scene of the movie Raiders of the Lost Ark, Indiana Jones replaces a golden statue with a bag of sand. The platform on which the statue is placed is designed to detect the mass of the statue. If the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues.
The density of gold is about 20\text{ g/cm}^320 g/cm
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20, start text, space, g, slash, c, m, end text, cubed. The density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm
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2, point, 5, start text, space, g, slash, c, m, end text, cubed. The solid-gold statue can be modeled as a cylinder with height 15\text{ cm}15 cm15, start text, space, c, m, end text and radius 4\text{ cm}4 cm4, start text, space, c, m, end text.
In terms of \piπpi, what is the volume of sand Indiana Jones needs to avoid triggering the mechanism?