Friday, May 10, 2013

Copper and Tin.

Questions on copper and tin

Copper costs around $3.3 per pound.   The density of copper is 8.94 (g/cm3).  What is the value of a cube of copper where each side of the cube is 15 cm?

Tin costs around $9.50 per pound.  The density of tin is 7.287 (g/cm3).   What is the size of a tin sphere with the same value as the copper cube?


First, lets convert the price of copper and tin from dollars per pound to $ per gram.  There are 453.6 grams in a pound.   Divide the price per pound units by the number of grams in a pound.

  • The price of copper is $7.28 x 10-3 per gram. 

  • The price of tin is $2.09 x 10 -2 per gram.

Seconds, let’s calculate the volume of the copper cube..

  • The cube of copper has a volume of 3375 cm3 (153).

Third, how much does the copper cube weight?

  • The cube weighs 30172.5 grams (3,375 cm3 x 8.94 (gm/cm3))

Fourth, what is the value of the cube?  Multiply weight in grams by price per gram.

  • The cube is worth $219.51 ($7.28x10-3 x 3.0172.5 x 104)

Fifth, let’s figure out how much a tin sphere worth $219.51 must weigh.

  • The weight of the tin sphere is $219.51/ $2.09 x 10-2 which is 10480.8 grams.   (We are dividing a unit in $ by a unit in $ per gram to get an answer in grams.)

Sixth, figure the size in cubic centimeters of a tin item that weighs 10480.8 grams. 

  • The volume of the sphere is 10480.8/7.287, which is 1438 cm3.  (We are dividing grams by grams/cm3 to get cm3.)

Seventh, figure out the radius of a sphere that has a volume of 1438.3 cm3. (This follows directly from the formula for the volume of a sphere, V=4/3 x pi x r3. )

  • The radius r is 7.003 cm.  (1438.3 /((4/3) x pi))1/3

I definitely need to check this answer.  There is likely to be some acceptable level of rounding error.  Let’s go backwards.

  • Volume of a sphere with a radius of 7.003 is 1438.6  (Plug 7.003 into sphere volume formula.)
  • The weight of the tin sphere is (1438.6x 7.287) or 10,483.1 grams.
  • The value of the sphere is $219.10. (10483.1 x 2.09x 10-2)

There appears to be a $0.40 rounding error.

If you enjoyed this post you may want to examine the post on the value of a box of platinum.

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