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Chemistry Help! How many pennies would it take to cover the earth with a single layer of pennies?

  • One mole of pennies would cover Earth's entire surface to a depth of 300m. How many pennies would be necessary to cover the Earth with a single layer of pennies? The diameter of a penny is 19.05mm and the radius of earth is 6378.1km. Approximate earth as a perfect sphere. And one more question relating to this if you guys could help :) If Earth was covered in pennies to a depth of 3.0*10^2, how many moles of pennies would there be in the topmost, complete layer? Thanks in advance guys! And please show me how you figured out the answer. I'm completely lost on how to do this.

  • Answer:

    I'm assuming that the pennies are touching edge-to-edge so that there will be some empty space between the pennies. In that case, each penny would effectively occupy the size of a square with sides equal to the diameter of the penny (19.05 mm). The area of this square = (19.05 mm)^2 = 363 mm^2 The surface area of a sphere is given by (4)(pi)(r^2). Radius of earth = 6378.1 km. 6378.1 km x (1000 m / 1 km) x (1000 mm / 1 m) = 6.38 x 10^9 mm Surface area of earth = (4)(pi)(r^2) = (4)(3.14)(6.38 x 10^9 mm)^2 = 5.11 x 10^20 mm^2 5.11 x 10^20 mm^2 x (1 penny / 363 mm^2) = 1.41 x 10^18 pennies!!! If you assumed that the pennies covered every bit of surface (i.e. there is no empty space between them), then the number would change to 1.79 x 10^18 pennies, assuming a penny area of (pi)(r)^2 = (3.14)(9.53 mm)^2 = 285 mm^2. ======================================... I can't answer part 2 since you gave me no units on the quantity (3.0 x 10^2). m? mm? If you mean m, 300 m, then you'd still have to know the thickness of the penny to solve the problem.

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Well, that would be a hell of a lot of pennies.

Shelby

Well, that would be a hell of a lot of pennies.

Shelby

I'm assuming that the pennies are touching edge-to-edge so that there will be some empty space between the pennies. In that case, each penny would effectively occupy the size of a square with sides equal to the diameter of the penny (19.05 mm). The area of this square = (19.05 mm)^2 = 363 mm^2 The surface area of a sphere is given by (4)(pi)(r^2). Radius of earth = 6378.1 km. 6378.1 km x (1000 m / 1 km) x (1000 mm / 1 m) = 6.38 x 10^9 mm Surface area of earth = (4)(pi)(r^2) = (4)(3.14)(6.38 x 10^9 mm)^2 = 5.11 x 10^20 mm^2 5.11 x 10^20 mm^2 x (1 penny / 363 mm^2) = 1.41 x 10^18 pennies!!! If you assumed that the pennies covered every bit of surface (i.e. there is no empty space between them), then the number would change to 1.79 x 10^18 pennies, assuming a penny area of (pi)(r)^2 = (3.14)(9.53 mm)^2 = 285 mm^2. ======================================… I can't answer part 2 since you gave me no units on the quantity (3.0 x 10^2). m? mm? If you mean m, 300 m, then you'd still have to know the thickness of the penny to solve the problem.

HPV

I'm pretty sure that someone will make the calculation for you (I'm too lazy laying in my bed before sleep with my phone) but I want to point out the fact, that if we speak about pennies as coins used as currency, you can not cover entire Earth's surface with single layer. The circular shape of penny would cause gaps in the penny layer. The simple x/y=z, where x is surface of Earth, y surface of penny and z number of pennies would not work.

Peter

Using the radius, calculate the surface area of the earth and divide that by the surface area of the penny. That will tell you how many pennies.---alot of pennies 4xpiexr^2 will be the formula It's not a perfect world, but if it was your answer (is) the (Answer) x/y=a do your measurement conversions

Teresa and Joe S

I'm pretty sure that someone will make the calculation for you (I'm too lazy laying in my bed before sleep with my phone) but I want to point out the fact, that if we speak about pennies as coins used as currency, you can not cover entire Earth's surface with single layer. The circular shape of penny would cause gaps in the penny layer. The simple x/y=z, where x is surface of Earth, y surface of penny and z number of pennies would not work.

Peter

Using the radius, calculate the surface area of the earth and divide that by the surface area of the penny. That will tell you how many pennies.---alot of pennies 4xpiexr^2 will be the formula It's not a perfect world, but if it was your answer (is) the (Answer) x/y=a do your measurement conversions

Teresa and Joe S

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