Finding density of a sphere and percentage error

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SUMMARY

The density of a sphere with a diameter of 4 cm and a mass of 1.35 grams is calculated to be 0.040 g/mL using the formula Density = Mass/Volume, where Volume is determined by the equation Volume = 4/3 x π x r³. The percentage error, comparing this calculated density to the actual density of 7.87 g/mL, is -99.50%. It is crucial to maintain consistent units throughout the calculations, as the resulting density is expressed in g/cm³, which is equivalent to g/mL.

PREREQUISITES
  • Understanding of basic geometry, specifically volume calculations of spheres
  • Familiarity with density calculations (Density = Mass/Volume)
  • Knowledge of percentage error calculations
  • Ability to convert units between g/cm³ and g/mL
NEXT STEPS
  • Study the derivation and application of the volume formula for spheres
  • Learn about the significance of density in material science
  • Explore advanced error analysis techniques in experimental physics
  • Investigate the relationship between mass, volume, and density in different states of matter
USEFUL FOR

Students in physics or chemistry, educators teaching density and volume concepts, and anyone involved in experimental data analysis and error calculation.

theherowithin
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1. What is the Density in g / mL of a sphere with a diameter of 4 cm and a mass of 1.35 grams?

What is the percent error if the actual density of the sphere was 7.87 g / mL?



2.Volume= 4/3 x pie x r cubed
Density= mass/volume
percentage error= result minus accepted divided by acceptd multiplied by 100

3. 4/3 x pie x 2 (cubed) =33.510
1.35/33.510= .040
.040-7.87/7.87 x 100= -99.50
 
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Carry the units through in your calculation to make sure they match the desired units, in this case you will want to end up with a density expressed in g/mL. Notice that the units you end up with in your calculation for density is g/cm^3. Hope this helps.
 

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