Visible Stars in the Night Sky

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The number of visible stars in the night sky, T, can be estimated by the formula

where N is the number of stars counted through a tube with length L, in centimeters, a mouth of area A, in square centimeters. Based on the formula, what is the estimated number of visible stars in the night sky if 240 stars are observed through a tube 10 feet long with a mouth of radius of 4 feet? (1 foot = 30.48 centimeters)

Review: Visible Stars in the Night Sky


Explanation

This question boils down to careful plugging. First, we need to get L and the radius in the right units:





We can calculate the area A from the radius. Let's not be too eager to multiply those numbers, however:



Now, we plug everything into the main formula and simplify as much as possible before computing:









The correct answer is (C).


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