# density of an unknown solid? **URL:** \ **Category:** Factual Questions\ **Created:** [December 16, 2002, 8:13pm UTC](https://boards.straightdope.com/t/density-of-an-unknown-solid/143151 "2002-12-16T20:13:44Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![SlickRoenick](https://avatars.discourse-cdn.com/v4/letter/s/e68b1a/32.png) [@SlickRoenick](https://boards.straightdope.com/u/SlickRoenick)\ **Post date:** [December 16, 2002, 8:13pm UTC](https://boards.straightdope.com/t/density-of-an-unknown-solid/143151/1 "2002-12-16T20:13:44Z")
Here’s a good practical question for the mathematicians and chemists and physicists: You mass an unknown solid in a small empty aluminum cup (87.893g) You mass a flask with it’s stopper (174.732g) You fill the flask completely with alcohol making sure no bubbles are in the flask and remass (431.451g) You insert the solid into the flask, replace the stopped, and remass the flask with alcohol and solid (515.642g) You know the density of the alcohol to be .813 g/mL What is the density of the solid? I found it out to be around 8.5 g/mL. But I might have some percentage error. I used the method of Density = Mass / Volume to get that answer. But I’m not sure if my answer is even right. Any dopers wanna give this a shot? ---
**Author:** ![GTPhD1996](https://avatars.discourse-cdn.com/v4/letter/g/97f17d/32.png) [@GTPhD1996](https://boards.straightdope.com/u/GTPhD1996)\ **Post date:** [December 16, 2002, 9:04pm UTC](https://boards.straightdope.com/t/density-of-an-unknown-solid/143151/2 "2002-12-16T21:04:27Z")
Muldoon Your information is incomplete. How did you measure the volume of the object? Is the flask graduated so you can measure the volume of a liquid inside it? What was the shape of the unknown solid? Was it a familiar shape such as a cylinder or cube that you could make measurements and calculate the volume from the known volume formula? GTPhD1996 ---
**Author:** ![SlickRoenick](https://avatars.discourse-cdn.com/v4/letter/s/e68b1a/32.png) [@SlickRoenick](https://boards.straightdope.com/u/SlickRoenick)\ **Post date:** [December 16, 2002, 9:11pm UTC](https://boards.straightdope.com/t/density-of-an-unknown-solid/143151/3 "2002-12-16T21:11:00Z")
According to the paper I have, the information is all there. I’m assuming I made up a number somewhere. . . should have written this down instead of just using a calculator. . . The flask is said to be an “Erlenmeyer Flask” and the solid doesn’t say anything regarding shape. If it helps the temperature of the alcohol is also given as 25.5 Celsius. ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [December 16, 2002, 9:17pm UTC](https://boards.straightdope.com/t/density-of-an-unknown-solid/143151/4 "2002-12-16T21:17:17Z")
Isn’t this essentially a derivation of [this story](http://www.sciencenet.org.uk/Origins/eureka.html) > [@](#): > > Although many of our discoveries were the result of serendipity, the first recorded example of an accidental discovery is in third century BC Greece. > > The king of Syracuse, Hiero, suspected his new gold crown was not pure gold. He called on the services of the mathematician Archimedes to lay his fears to rest. Archimedes knew that to find what the crown was made of he would need to work out the volume of an irregular solid. Then when he stepped into the bath he noticed water spilling over the top, and suddenly realised that the volume of the spilt water was equal to his bulk. So if he put the crown into water he could find its volume. Then he had to obtain a block of pure gold the same weight as the crown. If the volume was the same then the crown was gold, not an alloy. Archimedes jumped out the bath and ran naked through the streets of Syracuse shouting ‘Eureka, eureka!’ – ‘I’ve found it!’ ---
**Author:** ![The\_Flying\_Dutchman](https://avatars.discourse-cdn.com/v4/letter/t/9fc348/32.png) [@The\_Flying\_Dutchman](https://boards.straightdope.com/u/The_Flying_Dutchman)\ **Post date:** [December 16, 2002, 9:31pm UTC](https://boards.straightdope.com/t/density-of-an-unknown-solid/143151/5 "2002-12-16T21:31:17Z")
You are missing information. The solid could have more volume and be less dense and you could still get the same total mass in the end. You could remove the solid again though and re mass the somewhat lesser filled flask for a very good approximation of the displace mass, hence displaced alccohol volume hence volume of solid hence density of solid. ---
**Author:** ![micco](https://avatars.discourse-cdn.com/v4/letter/m/5f8ce5/32.png) [@micco](https://boards.straightdope.com/u/micco)\ **Post date:** [December 16, 2002, 9:37pm UTC](https://boards.straightdope.com/t/density-of-an-unknown-solid/143151/6 "2002-12-16T21:37:03Z")
I took your first mass to be the mass of the object. You don’t provide the mass of the small aluminum cup to subtract from that. Let V = volume of object = volume of alcohol displaced by object mass of object + surrounding alcohol/flask = 515.642 g mass of V alcohol + surrounding alcohol/flask = 431.451 g (mass of object) - (mass of V alcohol) = 515.642 - 431.451 = 84.191 g (mass of V alcohol) = 87.893 - 84.191 = 3.702 g V = (mass of V alcohol)/(density of alcohol) = 4.554 ml (density of object) = 87.893 g / 4.554 mL = 19.3 g/ml ---
**Author:** ![SlickRoenick](https://avatars.discourse-cdn.com/v4/letter/s/e68b1a/32.png) [@SlickRoenick](https://boards.straightdope.com/u/SlickRoenick)\ **Post date:** [December 16, 2002, 10:35pm UTC](https://boards.straightdope.com/t/density-of-an-unknown-solid/143151/7 "2002-12-16T22:35:49Z")
Wow micco, that’s good work. And I understand it too, thanks.