Question

"a u.S. 1-cent coin (a penny) has a diameter of 19 mm and a thickness of 1.5 mm". Assume the coin is made of pure copper, whose density and approximate market price are 8.9 g/cm3 and $2.15 per pound, respectively.

Answer 1

the question is Calculate the value of the copper in the coin

Step 1

Find the volume of the coin

we know that

the volume of a cylinder is equal to

`V=\pi r^(2)h`

where

r is the radius of the coin

h is the thickness of the coin

in this problem we have

Diameter=19 mm=1.9 cm

r=D/2------> r=1.9/2=0.95 cm

h=1.5 mm=0.15 cm

substitute the values in the formula

`V=\pi*0.95^(2)*0.15=0.425\ cm^(3)`

Step 2

Find the mass of copper in the coin

we know that

the density is equal to

`Density=mass/volume`

Solve for the mass

`mass=Density*volume`

we have

`Density=8.9\ gr/cm^(3)\\Volume=0.425\ cm^(3)`

substitute in the formula

`mass=8.9*0.425=3.785\ gr`

Step 3

Find the cost

we know that

the market price of the copper is $2.15 per pound

1 pound=453.592 grams

convert gram to pounds

3.785 gr=3.785/453.592=0.0083 pounds

0.0083*$2.15=$0.018=$0.02

therefore

the answer is

$0.02