Find the number of elements in a1 ∪a2 ∪a3 if there are 100 elements in a1, 1000 in a2, and 10,000 in a3 if a) a1 ⊆ a2 and a2 ⊆ a3. b) the sets are pairwise disjoint. c) there are two elements common to each pair of sets and one element in all three sets.

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?