Korach- Equally Shared Surface Area

"Hashem spoke to Moshe, saying, "Say to Elazar son of Aaron the pans from amid the blaze- and he should move away the fire- for they have become holy. As for the fire-pans of these sinners against their souls- they shall make them thinned-out sheets as a covering for the Altar, for they offered them before Hashem, so they became holy; they shall be for a sign to the Children of Israel." ~Bamidbar 17;1-3

In this week's parsha, we learn that Elazar is told to collect the fire-pans belonging to Korach and his followers, thin out the pans, and make a covering for the Copper Alter out of the thinned fire-pans. On reading this directive, I wondered how much area each pan actually covered once it was thinned out. 

If we look back in Shemot 27;1-2, we can remember the description of the Copper Altar:
"You shall make the Mizbe'ach of shittim wood, five amot long and five amot wide- the Mizbe'ach shall be square- and three amot its height. You shall make its horns on its four corners, from it shall its horns be; and you shall cover it with copper."

Back in Parshat Terumah we looked at how to calculate surface area. Multiplying the length x width  gives us the measurement of square area, telling us how much flat space is covered. Using this calculation, and knowing from Shemot that the Copper Altar is 5 amot long and 5 amot wide, we can calculate that the area of the altar was 25 square amot. 

The next step is to figure out how big a section from the 25 square amot came from each fire-pan. To find this out, we need to divide the area by the number of fire-pans. There were 250 men with Korach, which means that Elazar had to thin out 250 fire-pans in order to cover 25 square amot. So, we divide 25 square amot ÷ 250 pans = 1/10 square amah per fire-pan. In other words, each thinned out fire-pan covered an area of .1 square amot. 

Everyday Connections:
For our reference, how big is that? An Amah is estimated between 18-24 inches. We can repeat our calculations with these two estimated lengths to have an idea of a range of the size of the fire-pans. 
Assuming 1 Amah = 18 in
The length and width of the altar were each 90 in 
90 x 90 = 8,100 square inches for the area of the top of the altar
8100 ÷ 250 = 32.4 square inches per fire-pan

Assuming 1 Amah = 24 in
The length and width of the altar were each 120 in 
120 x 120 = 14,400 square inches for the area of the top of the altar
14,400 ÷ 250 = 57.6 square inches per fire-pan

So, from these calculations, each fire-pan was able to be thinned out to between 32.4-57.6 square inches. This means that each fire pan was only able to be thinned out to between 5.5-7.5 inches along each side if they were flattened into perfect squares. So, the final thinned out pieces were smaller than the bottom of an 8 x 8 baking pan. Imagine how small they must have been before they were thinned out!

An extra thought- What if the covering that Hashem required was supposed to cover the entire altar rather than just the top? Using surface area calculations from Parshat Terumah, how large would the surface area have been? How much bigger would each fire-pan have been with these new calculations?