Answer :
Answer:
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:
[tex] V_{i} = \frac{1}{2}*\frac{4}{3}\pi r_{i}^{3} [/tex]
[tex] V_{o} = \frac{1}{2}*\frac{4}{3}\pi r_{o}^{3} [/tex]
The total volume is given by:
[tex] V_{T} = V_{o} - V_{i} [/tex]
Where:
[tex] V_{i} [/tex]: is the inner volume
[tex]r_{i}[/tex]: is the inner radius = 1.25/2 = 0.625 m
[tex] V_{o} [/tex]: is the outer volume
[tex]r_{o}[/tex]: is the outer radius = 1.45/2 = 0.725 m
Then, the total volume of the Igloo is:
[tex] V_{T} = \frac{2}{3}\pi r_{o}^{3} - \frac{2}{3}\pi r_{i}^{3} = \frac{2}{3}\pi [(0.725 m)^{3} - (0.625 m)^{3}] = 0.29 m^{3} [/tex]
Now, by using the density we can find the mass of the Igloo:
[tex] m = 19.3 \frac{g}{cm^{3}}*0.29 m^{3}*\frac{(100 cm)^{3}}{1 m^{3}} = 5.60 \cdot 10^{6} g [/tex]
Finally, the value (V) of the antiquity is:
[tex] V = \frac{\$ 1263}{oz}*5.60 \cdot 10^{6} g*\frac{1 oz}{31.1034768 g} = \$ 227.4 \cdot 10^{6} [/tex]
Therefore, the value of the Golden Igloo is $227.4 million.
I hope it helps you!