1. Archaeologists have discovered the legendary Golden Igloo of the Pribiloff Islands, a structure consisting of a

halfspherical shell with an inner diameter of 1.25 m and an out diameter of 1.45 m. What is the value of this antiquity,

given that gold currently sells for $1,263/ounce and has a density of 19.3 g/cm3? (Note that 1 ounce = 31.1034768 g)

The value of the Golden Igloo is $227.4 million.

Explanation:

First, we need to find the inner and the outer volume of the half-spherical shell:

The total volume is given by:

Where:

: is the inner volume

: is the inner radius = 1.25/2 = 0.625 m

: is the outer volume

: is the outer radius = 1.45/2 = 0.725 m

Then, the total volume of the Igloo is:

Now, by using the density we can find the mass of the Igloo:

Finally, the value (V) of the antiquity is:

Therefore, the value of the Golden Igloo is $227.4 million.

I hope it helps you!  

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