Maths - the king asked archimedes if his crown is made from pure gold he knows that the crown is?

... either pure gold or it may have some silver in it .archimedes figures out that the volume of the crown is 125 cm cubed and the mass is 1.8 kilogr

... either pure gold or it may have some silver in it .
archimedes figures out that the volume of the crown is 125 cm cubed and the mass is 1.8 kilograms.
he also knows that 1 kilogram of gold has a volume of about 50cm cubed and 1 kilogram of silver has a volume of about 100 cm cubed
is the crown pure gold why or why not?

or:... either pure gold or it may have some silver in it .archimedes figures out that the volume of the crown is 125 cm cubed and the mass is 1.8 kilograms.he also knows that 1 kilogram of gold has a volume of about 50cm cubed and 1 kilogram of silver has a volume of about 100 cm cubedis the crown pure gold why or why not?

or:i dont think its pure gold .... It all depends on density .... Density = mass/volume density of pure gold : 1/50 =.02kg/cm^3density of silver is 1/100=.01kg/cm^3what about crown ... Its mass = 1.8kg, its volume = 125cm^3so its density=1.8/125=.0144kg/cm^3

or:1g = 1 gram = 1kg / 10001ccm = 1 cm^3 = 1 centimeter cubedeq. = short for equationu = gold, aUrumr = silver, aRgentum\u03c1 = rho, density = mass / volumeAccording to the accompanying text of the assignment the density of - gold is: \u03c1_u = 1000g / 50ccm = 20g / ccm- silver is: \u03c1_r = 1000g / 100ccm = 10g / ccm- the crown's alloy is: \u03c1_crown = 1800g / 125ccm = 14.4g / ccmthereby telling us that\u03c1_r < \u03c1_crown < \u03c1_u.The crown, therefore, cannot be made of pure gold. So far, so easy.But now it's getting interesting. The king's curiosity is excited and he inquires of Archimedes ...Well, actually, I thought this purely qualitative answer to be rather unsatisfying. But as, unfortunately for us, Archimedes doesn't happen to be with us anymore, we are on our own. It's not that tough though, in fact, it's quite straight forward; so let's do this.Question 1:This will be related to the mass of the crown. We need an eq. which describes, how many ccm of gold with 20g/ccm each plus how many ccm of silver with 10g/ccm each equals the mass of the crown.u ccm * 20g/ccm + r ccm * 10g/ccm = 1800g ;; the ccm cancel just outu * 20g + r * 10g = 1800g ;; simplify further: divide by 10gEq. 1) 2u + r = 180-------------------------Question 2:This will be related to the volume of the crown.The second eq. has to describe how the volume of gold plus the volume of silver equals the volume of the crown.u ccm + r ccm = 125ccm ;; divide by ccmEq. 2) u + r = 125-----------------------(Each eq. alone has infinitely many solutions, but as we are going to solve them simultaneously, they constitute a system of mutually constrained parts.)Eliminate r from the system of eq.s:Eq. 3) = 1) - 2)u = 55Inserting this in eq. 2 yieldsr = 70And as we described the volume there, we know now:55ccm of gold + 70ccm of silver = 125ccm, the volume of the crown.-----------------------------------------------------------------------------Inserting these values into the mass related eq.u * 20g + r * 10g = 1800g yields55 * 20g + 70 * 10g = 1800g1100g of gold + 700g of silver = 1800g, the mass of the crown.

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