more density

My book has half a page where it talks about density and it only says that density=mass/volume. my question is...
1. in each of the following pairs which has the greater volume?
A) 1.0kg of feathers or 1.0kg of lead
B)100g gold or 100g of water
C) 1.0L of copper or 1.0L of mercury
Do I need to convert first?

2. A copper wire (density= 8.96g/cm^3. If a 1.00kg rectangular block of osmium has two dimensions of 4.00 x 4.00 cm, calculate the third dimension of the block.

3. which has greater mass
A) 1.0kg of feathers or 1.0kg of lead
B) 1.0ml of mercury or 1.0ml of water
C) 19.3ml of water or 1.00 ml of gold
D) 75ml of copper or 1.0L of mercury
Do I have to convert these also? and how? I dont know how to convert to cm^3 and g/cm^3 HELP ME PLEASE. I HAVE TO KNOW THESE EQUATIONS FOR TOMMOROWS RECITATION. THANK YOU!

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You really don't have to convert anything; just use some common sense.

In 1, the greater volume will be found in entities with the greater density when they have the same mass (parts A and B); if the entities have the same volume, they will have the same volume (part C); this is a stupid trick question intended to make sure you know the difference between units of mass and volume.

2 doesn't make much sense babbling about Cu wire, but if it is asking how much Os is needed, check the density of osmium, then calculate the volume of one kilo of Os in cc./mL. A cubic meter of osmium would make you very, very rich and weigh about 22,610 kg; you now have an equation that 22,610kg /1,000,000 cc = 1 kg/X cc. To solve for X cc, multiply 1,000,000 cc x 1 kg and divide by 22,610 kg. Then divide the answer by 16 cm2, the answer is the third dimension of your right rectangular prism of a much more affordable chunk of Os.

3 is a more complex reprise of 1; A have the same mass, so they have the same mass; B has the same volumes so the denser substance has more mass; for C, the density of water is the standard for 1 (presuming that these are at STP, if it is a very hot day some complexities come into play but I doubt that your textbook or teacher are that clever) and it so happens that if you look up the density of Au, you will find that it is 19.3, meaning that one volume of Au is 19.3 times as heavty as water, or that you need 19.3 times as much water to equal the same volume of Au thus 1 mL of Au and 19.3 mL of water have the same mass. D You know that 1 liter = 1000 mL; therefore with 75 mL of Cu you have a volume = .075 of that of Hg; unless the density of Cu is much greater than Hg (trust me it isn't) the much larger volume of much denser Hg with have the greater mass.

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