Find Rho of Hollow Cylinder: Explaining Formula & Solving

In summary, the formula for finding the density of a hollow cylinder involves 4 measured quantities (mass, outside diameter, inside diameter, and height) and is given by ρ = (4m)/(π(d²-D²)h). This can also be derived from the formula for the area of a circle, A = (π/4)(d²-D²).
  • #1
mtje
1
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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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  • #2
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.
 

Related to Find Rho of Hollow Cylinder: Explaining Formula & Solving

1. What is the formula for finding the density (rho) of a hollow cylinder?

The formula for finding the density of a hollow cylinder is rho = (m1 - m2) / (V1 - V2), where m1 and m2 are the masses of the cylindrical shell and the inner cylinder, respectively, and V1 and V2 are the corresponding volumes.

2. How do you solve for the density of a hollow cylinder?

To solve for the density of a hollow cylinder, you need to know the masses and volumes of both the cylindrical shell and the inner cylinder. Once you have these values, you can plug them into the formula rho = (m1 - m2) / (V1 - V2) and solve for rho.

3. Can the mass or volume of a hollow cylinder be negative?

No, the mass and volume of a hollow cylinder cannot be negative. The mass and volume are physical quantities that represent the amount of matter and space, respectively, and cannot have negative values.

4. How does the density of a hollow cylinder compare to that of a solid cylinder?

The density of a hollow cylinder is generally lower than that of a solid cylinder, since a hollow cylinder has a larger volume than a solid cylinder with the same mass. This means that the same amount of matter is spread out over a larger space, resulting in a lower density.

5. What is the significance of finding the density of a hollow cylinder?

Finding the density of a hollow cylinder is important in various scientific fields, such as physics and engineering. It allows us to understand the physical properties of the cylinder, such as its mass and volume, and can be used to calculate other important quantities, such as the buoyancy force acting on the cylinder.

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