How do you calculate/find mass, volume?

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To find mass and volume, use the formula density = mass/volume. For the first question, with a density of 50 kg/m³ and dimensions of 2m x 2m x 5m, calculate the volume first, which is 20 m³, then multiply by the density to find mass, resulting in 1000 kg. For the second question, with a density of 6 kg/m³ and a mass of 22 kg, divide mass by density to find volume, which equals approximately 3.67 m³. The key operations involve multiplying or dividing based on the relationship between mass, volume, and density. Understanding the units involved is crucial for accurate calculations.
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I did my homework and there are some bonus questions that we really never learned about in class, if we get them right it adds to the mark, it says find mass and volume and things, any help?
 
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density = mass/volume
 
The question is, A material has a density of 50kg/m cubed, and sides that measure 2m, 2m, and 5m, find the mass

other is

A material has a density of 6 kg/m cubed, and a mass of 22kg, find the volume,

For the second question would you multiple density and mass, or divide?
 
brysonlee said:
The question is, A material has a density of 50kg/m cubed, and sides that measure 2m, 2m, and 5m, find the mass

other is

A material has a density of 6 kg/m cubed, and a mass of 22kg, find the volume,

For the second question would you multiple density and mass, or divide?

Forget the numbers for a moment and just look at the units of each quantity. If you perform the operations that you indicate (multiplying density and mass, dividing density by mass), what are the units of the results?
 
iRaid gave the basic information, and there is enough information in your problem descriptions to find the basic parts that you need to work with.

Your first question shows enough information to calculate the volume, so you have enough to find mass. The second question gives mass but asks for volume. Either case, you use the same basic relationship:

Letting m = mass, v = volume, d = density, you rely on any equivalent equation for
d = \frac{m}{v}
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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