How Do You Calculate the Mass of an Osmium Sphere?

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SUMMARY

To calculate the mass of an osmium sphere with a diameter of 15 cm, first determine the radius, which is 7.5 cm. Using the formula for the volume of a sphere, V = 4/3 * π * (radius)^3, the volume calculates to approximately 1767.15 cm³. Given that the density of osmium (Os) is 22.57 g/cm³, the mass can be found using the formula mass = density * volume, resulting in a mass of approximately 39.87 kg.

PREREQUISITES
  • Understanding of basic geometry, specifically the volume of a sphere
  • Knowledge of density and its relationship to mass and volume
  • Familiarity with the mathematical constant π (pi)
  • Basic unit conversions between grams and kilograms
NEXT STEPS
  • Study the formula for the volume of a sphere in more detail
  • Learn about unit conversions, specifically between grams and kilograms
  • Explore the properties of osmium, including its density and applications
  • Practice problems involving density, mass, and volume calculations
USEFUL FOR

This discussion is beneficial for students studying chemistry or physics, educators teaching these subjects, and anyone interested in understanding the calculations related to density and volume in real-world applications.

Mootiek
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I am having trouble with how to set up the equation for this problem...

Os is the densest element known. Given that the density of Os is 22.57g/cm^3, calculate the mass, in kg, of an Os sphere 15 cm in diameter, which is about the size of a grapefruit.

Any help would be greatly appreciated. I am really confused with where the diameter fits in... I feel so lost in this class! Yikes!
 
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You need to work on the basics:
Volume of a sphere = 4/3( pi ) (radius cubed)
Density = mass/volume
 

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