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A steel ball-bearing with a ˚umference of 32.5 mm weighs 4.20 g. What is the density of the steel in g/cm³? (Volume of a sphere = 4/3πr 3 , ˚umference of a ˚le = 2πr)
A steel ball-bearing with a ˚umference of 32.5 mm weighs 4.20 g. What is the density of the steel in g/cm³? (Volume of a sphere = 4/3πr 3 , ˚umference of a ˚le = 2πr)a) 2.56 g/cm³
b) 1.28 g/cm³
c) 0.64 g/cm³
d) 0.32 g/cm³
Final answer:To find the density of the steel, calculate the radius from the given circumference, compute the volume using the radius, and apply the density formula using the given mass.Explanation:The question is asking to calculate the density of the steel ball-bearing using its given circumference and weight.First, we need to find the radius of the ball-bearing from its circumference. The formula for the circumference (C) of a circle is C = 2πr, where r is the radius. We rearrange the formula to solve for r: r = C / (2π). Substituting the given circumference of 32.5 mm, we obtain the radius in millimeters. We then convert the radius to centimeters to be consistent with the volume formula V = (4/3)πr^3, which is in cubic centimeters (cm³).After calculating the volume, we use the formula for density (ρ) which is ρ = mass/volume. The mass of the ball-bearing is given as 4.20 g. We calculate the density with the mass in grams and the volume in cubic centimeters to get the result in the desired unit of g/cm³....