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 $2.40 per pound, respectively. Calculate the value of the copper in the coin, assuming its thickness is uniform.

Video transcript

Hi everyone here we have a question telling us that the American Silver Eagle is the official silver bullying coin of the United States. It has a diameter of 40.6 mm and a thickness of 2.98 mm. Silver has a density of 10.49 g per cm cubed and is valued at 365 $.90 per pound, assuming that the coin has a uniform thickness and is made of pure silver, calculate the value of the coin. So our diameter is 40. millimeters. And to get the radius, we're going to divide that by two. So our radius equals 20.3 mm Which is equal to 2.03 cm and our density equals 0.49 grams per centimeters cubed. Our height Is 2.98 mm Which equals 0. cm. And we're going to use the equation density equals mass over volume. And we are going to plug in for volume. Our equation to solve for volume. So P equals mass over Hi times radius squared times height. And we're going to isolate mass. So mass equals density times pi times radius squared times high. And now we're going to plug in what we know. So mass equals 10.49 grams per centimeters cubed, times pi Times 2. centimeters. And that is squared Times 0.298 cm And that equals 40.45 g. Now we need to convert so we have one kg Equals £2.. and one kg Equals 10 to the 3rd g. So our mass is going to equal .45 g times one kg Over 10 to the 3rd Graham Times £2.. over one kg. And our grams cancel out and our kilograms cancel out, giving us zero point zero £89. And then we have 0.089 lbs. And we want to change that $2. So times our $90.90 over £ and our pounds are canceling out, And that equals $ And 56 cents. And that is our final answer. Thank you for watching. Bye.