**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?

**Answers**:

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 cm
^{3}(15^{3}).

Third, how much does the copper cube weight?

- The cube weighs 30172.5 grams (3,375 cm
^{3}x 8.94 (gm/cm^{3}))

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 cm
^{3}. (We are dividing grams by grams/cm^{3}to get cm^{3}.)

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 r

^{3}. )- 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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