zmVault/pumpkin-coins-estimate.md

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id	aliases	tags	title	dg-publish
		topic/estimating type/idea	Pumpkin Coins Estimate	true

Pumpkin Coins Estimate

Announcement

[!quote] ... There's a pumpkin filled with coins just waiting for someone to nail the number. Think you've got what it takes to guess the total value inside?

💰 Guess the Dollar Value in the Pumpkin

...

🕒 All votes due by 3:00 PM on Wednesday, 10/29

Bring your best guess---the closest estimate wins big! ...

Strategy

Expected Coin

Estimate expected value and volume for a randomly selected coin.

Coin		Frequency F	Monetary Value M	Radius r	Thickness h	Volume V
Quarter			0.25
Dime			0.10
Nickel			0.05
Penny			0.01

V = \pi r^2 \times h

Expected Monetary Density

D = \frac{M_{E}}{V_{E}} \times E

where

• M_{E} = Monetary value of the Expected Coin
• V_{E} = Cylindrical volume of the Expected Coin
• E = Packing efficiency

[!note] Estimating Packing Efficiency Estimating E will be tricky.

Volume of the "Bowl"

Let the "bowl" be a hemispherical volume with radius r_{B} enclosing all coins.

The volume of the bowl V_{B}, the liquid volume occupied by the coins, is given by

V_{B} = \frac{2}{3} \pi  r_{B}^3

Total Monetary Value

The total monetary value of all coins in the bowl is given by

\begin{align*}
M_{B} &= V_{B} \times D
\end{align*}