Discussion topicin this unit, you worked with geometric proofs. aproof is a logical sequence of justified conclusionsthat lead from a hypothesis to a final conclusion. in your opinion, why are mathematical proofsimportant? suppose that a conclusion within a proof isn'tjustified or is inaccurate. in geometry, what mightbe the consequences of the inaccuracy? now think about different kinds of proofs that takeplace outside the world of geometry, and list a fewexamples. what might be the consequences ofhaving an unjustified conclusion surface in suchproofs? who might be affected and how?

Nthe 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 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?