Answer: 74.8%
This answer is approximate.
The value is rounded to the nearest tenth of a percent.
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Explanation:
Let,
X = area of the larger circle
Y = area of the smaller circle
Z = area of the shaded region = X - Y
The goal is to compute the ratio Z/X to get the answer we want
Let's find area of the larger circle
Area of circle = pi*(radius)^2
A = pi*r^2
X = pi*8.01^2
X = 64.1601pi
This is the exact area in terms of pi
Now repeat for the smaller circle
A = pi*r^2
Y = pi*4.02^2
Y = 16.1604pi
Subtract those results to find the value of Z
Z = X-Y
Z = 64.1601pi-16.1604pi
Z = 47.9997pi
This is the exact area of the red donut region
Divide Z over X to get the probability of landing in the red region
Z/X = (47.9997pi)/(64.1601pi)
Z/X = (47.9997)/(64.1601) <--- note how the pi terms cancel
Z/X = 0.74812 which is approximate
Convert to a percent
Move the decimal point 2 spots to the right
0.74812 ---> 74.812%
Then round this to one decimal place
74.812% ---> 74.8%
36204 turns into 36200, and 40918 turns into 40920
A nickel has a diameter of 21.21 mm and a thickness of 1.95 mm
<span>2.121 cm diameter </span>
<span>0.195 cm thickness </span>
<span>Think of a nickel as a cylinder </span>
<span>r = 2.121/2 = 1.0605 cm </span>
<span>V = pi * r^2 * h </span>
<span>V = pi * 1.0605^2 * 0.195 cubic cm </span>
<span>2 liters = 2000 cubic cm </span>
<span>2000 / (1.0605^2 * 0.195 * pi) => </span>
<span>2902.84713216 </span>
<span>Your upper limit is 2902, but it could be as little as 0 (for instance if the 2L bottle was only 1 cm wide, then you wouldn't be able to fit a single nickel in there) </span>
<span>I'd say that you could expect about a 70% packing efficiency, just off the top of my head </span>
<span>2900 * 0.7 => </span>
<span>290 * 7 => </span>
<span>300 * 7 - 10 * 7 => </span>
<span>2100 - 70 => </span>
<span>2030 </span>
<span>I'd expect around 2000 nickels would fill up the bottle quite nicely, supposing you can get the nickels into it.</span>
You do 822.6 divided by 18
It is equal to 45.7
45.7 km per hour
