Calculate Density of Sphere: Mass, Diameter & Volume

You might want to check the problem statement to make sure you didn't miss anything.In summary, the volume of a sphere can be expressed as d^3 x pi / 6, and the density can be calculated as 6M/pi x d^3. However, it is important to double check the problem statement to ensure that all variables and equations are correct.
  • #1
anoel
5
0

Homework Statement



1.express the volume in terms of the diameter d of the sphere
2.write an equation to find the density of the sphere in terms of mass M and diameter d

Homework Equations



sphere Volume = 4 x pi x r^3 / 3
density = mass/volume


The Attempt at a Solution



1. d=2r so V = d^3 x pi / 6
2. density = M / V(=d^3 x pi /6) = 6M/pi x d^3



but my teacher said it is wrong. what is wrong with my answer?
 
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  • #2
Assuming you had density written up in your answer like [itex]\frac{6M}{\pi d^3}[/itex] or similar (in the post above you missed some parenthesis) in I don't see anything wrong.
 

1. What is the formula for calculating the density of a sphere?

The formula for calculating the density of a sphere is density = mass / volume. This means that the density of a sphere is equal to the mass of the sphere divided by its volume.

2. How do you calculate the mass of a sphere?

To calculate the mass of a sphere, you need to know its density and volume. You can then use the formula mass = density x volume to find the mass. Alternatively, if you know the diameter and density of the sphere, you can use the formula mass = (4/3)πr^3 x density, where r is the radius of the sphere.

3. Can the density of a sphere change?

Yes, the density of a sphere can change if its mass or volume changes. For example, if more material is added to the sphere, its mass will increase, causing the density to increase. Similarly, if the volume of the sphere is increased, the density will decrease.

4. What units are used to measure density?

The units used to measure density depend on the system of measurement being used. In the metric system, density is typically measured in grams per cubic centimeter (g/cm^3). In the imperial system, it is measured in pounds per cubic inch (lb/in^3).

5. How does the diameter of a sphere affect its density?

The diameter of a sphere does not directly affect its density. However, the diameter is used to calculate the volume of the sphere, which is a factor in the density formula. A larger diameter will result in a larger volume, which can lead to a lower density if the mass of the sphere remains the same.

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