Question concerning average density

In summary, a planet with a core of radius R/3 and density 2d, a middle layer from radius R/3 to 2R/3 and density d/2, and an outer shell from radius 2R/3 to R and a density of d will have an average density found by dividing the total mass of the sphere by its total volume, which can be calculated by finding the mass of each portion of the sphere and adding them together.
  • #1
Emethyst
118
0

Homework Statement


A planet or radius R has a core of radius R/3 and density 2d, a middle layer from radius R/3 to 2R/3 and density d/2, and an outer shell from radius 2R/3 to R and a density of d. What is the average density as a whole?



Homework Equations


d=m/v


The Attempt at a Solution


Not sure where else to stick this question so I put in the basic math section here (if it's the wrong section please do move it). I figured that to solve this question I would need to simple add all 3 density values given together and divide by 3. This seems too easy, however, and I'm not sure if I can treat the mass as a constant. Would this be the right method or am I missing something here? If anyone could be of assistance it would be greatly appreciated, thanks in advance.
 
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  • #2
Figure out the mass of each portion using m = dv then divide the total mass by the total volume to get the average density.
 
  • #3
No, adding all 3 density will not give you the "average" density. That would work only if all densities were for an equal volume. You need to use the basic definition of "density". Find the mass of the entire sphere and divide by its volume.

Multiply the density of each region by its volume (that is LCKurtz's formula). The first is easy- its volume the volume of a sphere of radius R/3. The second is trickier. Find the volume of a sphere of radius 2R/3 and then subtract the volume of a sphere of radius R/3. For the outer shell, find the volume of a sphere of radius R and subtract the volume of a sphere of radius 3R/3.
 

1. What is average density?

Average density is the measure of the amount of mass per unit of volume of a substance. It is calculated by dividing the mass of the substance by its volume.

2. How is average density different from specific gravity?

Specific gravity is the ratio of the density of a substance to the density of a reference substance, usually water. Average density, on the other hand, is the measure of the density of a substance on its own.

3. What units are used to measure average density?

Average density is typically measured in units of grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3). However, it can also be measured in other units such as pounds per cubic inch (lb/in3) or ounces per cubic inch (oz/in3).

4. How is average density important in science?

Average density is an important concept in science as it helps us understand the physical properties of different substances. It is used in various fields such as chemistry, physics, and geology to identify and classify materials, determine their buoyancy, and predict their behavior under different conditions.

5. How can average density be calculated for irregularly shaped objects?

To calculate the average density of an irregularly shaped object, its volume can be measured by displacement method. This involves placing the object in a container of water and measuring the amount of water it displaces. The mass of the object can then be divided by its volume to determine its average density.

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