Find Rho of Hollow Cylinder: Explaining Formula & Solving

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SUMMARY

The density (ρ) of a hollow cylinder can be calculated using the formula ρ = 4m / (π(d² - D²)h), where d is the outside diameter, D is the inside diameter, m is the mass, and h is the height. The formula for the volume (V) of the hollow cylinder is V = π(d² - D²)h, derived from the area of a circle. The factor of 4 in the numerator represents a specific adjustment in the formula for density calculation. Understanding these relationships is crucial for solving problems related to hollow cylinders in physics.

PREREQUISITES
  • Basic understanding of physics concepts, particularly density and volume.
  • Familiarity with geometric formulas, especially for circles and cylinders.
  • Knowledge of algebraic manipulation to rearrange formulas.
  • Experience with physics problems involving mass and volume calculations.
NEXT STEPS
  • Study the derivation of the volume formula for hollow cylinders.
  • Learn about the physical significance of density in material science.
  • Explore the application of density calculations in real-world engineering problems.
  • Investigate the relationship between mass, volume, and density in different shapes.
USEFUL FOR

Students taking introductory physics courses, educators teaching density and volume concepts, and anyone interested in understanding the properties of hollow cylindrical objects.

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Homework Statement



rho of a hollow cylinder can be found with 4 measured quantity by the folowing formula, proof this formula

Homework Equations

ρ= 4.m
∏.(d²-D²).h

d is the outside diameter and D the inside

The Attempt at a Solution



since it's my first time ever taking physics classes I'm kinda stuck
(well first time taking science classes:blushing:)

ρ=m
V

so the formula of the hollow cylinder is V=∏.(d²-D²).h

the 4.m should be the mass but don't really get what the 4 is standing there for

Could someone explain me how i should solve this ore give me a helping hand with the beginning of it?
 
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The formula for the area of a circle is

A = π r2 = (π/4) d2

where r = radius and d = diameter.

When you have a hollow circle, the same sort of thing still applies, just with a difference of squares. But notice the (π/4) stays out in front.

If you think this on through, you will see where the rest of your expression comes from.
 

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