Calculating Density of a Standard 1kg Weight: Step-by-Step Guide

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SUMMARY

The discussion focuses on calculating the density of a standard 1kg weight, which is a cylinder measuring 50.0 mm in height and 51.5 mm in diameter. The correct formula for density is established as density = mass/volume, with the volume of a cylinder calculated using the formula volume = πr²h. The initial calculation of volume was incorrect due to the omission of π, leading to a density calculation of approximately 3.01 x 10³ kg/mm³. Participants clarified the importance of π in the volume calculation.

PREREQUISITES
  • Understanding of basic geometry, specifically the properties of cylinders.
  • Familiarity with the formula for density: density = mass/volume.
  • Knowledge of the mathematical constant π (pi) and its significance in circular calculations.
  • Ability to perform unit conversions, particularly between mm³ and kg.
NEXT STEPS
  • Study the formula for the volume of a cylinder, including the role of π.
  • Learn about unit conversions between different measurement systems, such as mm³ to m³.
  • Explore density calculations for various shapes and materials.
  • Investigate the significance of precision in mathematical calculations and its impact on results.
USEFUL FOR

Students in physics or engineering courses, educators teaching geometry and density concepts, and anyone interested in understanding the mathematical principles behind volume and density calculations.

chocolatelover
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Hi everyone,

Homework Statement



A standard 1kg weight is a cylinder 50.0 mm in height and 51.5 mm in diameter. What is the density?

Homework Equations



density=mass/volume
volume of a cylinder=hr^2

The Attempt at a Solution



v=(50.0m)(51.5m/2)^2
=33153.125
=3.32 x 10^4 mm^3

density=1kg/3.32 X 10^4mm^3
=3012.048193
=3.01X10^3

Could someone please tell me if this is correct?

Thank you very much
 
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You are off by a factor of pi.
 
Thank you very much

What is pi?
 
The volume of a cylinder is the area of a circle times the height of the cylinder.

You seem to be asking a lot of questions here lately...
 
Thank you very much

Regards
 
chocolatelover said:
What is pi?

Uhhh... joke?

It's the ratio of the circumference of a circle to its diameter. pi = C/d ~ 3.141592...
 
Thank you very much
 

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