Question

If a stack of 45 coins fits snugly in the coin wrapper shown, how thick is 1 coin?

coin
wrapper
d=21.17 mm V=28,470 mm

Answer 1

1.797 mm

Explanation:

The key to solving this problem is finding the length of the coin wrapper, or "height" of the cylinder.

The volume of a cylinder equation is:

V = hπr^2

- We want to find h

- We are given diameter and we will want the radius so we divide

21.17/2 = 10.585

r = 10.585

So to find h we manipulate the equation by dividing both sides by pi and r^2

resulting in the following:

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

now substitute given values and we get

h =
`(28470)/(\pi10.585^(2) )` = 80.883

Now to find the thickness of a single coin we divide the length of the sleeve (h) by the number of coins in the sleeve (45).

Thickness = 80.883/45 = 1.797 mm