What is the quantity of lead necessary for the production of 100 spherical balls, solid, each with a diameter of 1 cm?

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Ed

To calculate the quantity of lead necessary for the production of 100 spherical balls, solid, each with a diameter of 1 cm, we can use the formula for the volume of a sphere: V = (4/3) * π * r³ Where V is the volume, π is the mathematical constant pi (approximately 3.14), and r is the radius of the sphere. Since the diameter of each ball is 1 cm, the radius is 0.5 cm. Substituting this value into the formula, we get: V = (4/3) * π * (0.5 cm)³ V = (4/3) * π * 0.125 cm³ V = 0.5236 cm³ The volume of one ball is 0.5236 cm³. To find the total volume of 100 balls, we multiply this value by 100: V_total = 0.5236 cm³ * 100 V_total = 52.36 cm³ Finally, we need to convert the volume to mass, using the density of lead. The density of lead is approximately 11.34 g/cm³. Therefore: mass = density * volume mass = 11.34 g/cm³ * 52.36 cm³ mass = 596.8 g So, the quantity of lead necessary for the production of 100 spherical balls, solid, each with a diameter of 1 cm is approximately 596.8 grams.