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.