Question

1.

Answer 1

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:

$V_{i} = \frac{1}{2}*\frac{4}{3}\pi r_{i}^{3}$

$V_{o} = \frac{1}{2}*\frac{4}{3}\pi r_{o}^{3}$

The total volume is given by:

$V_{T} = V_{o} - V_{i}$

Where:

$V_{i}$: is the inner volume

$r_{i}$: is the inner radius = 1.25/2 = 0.625 m

$V_{o}$: is the outer volume

$r_{o}$: is the outer radius = 1.45/2 = 0.725 m

Then, the total volume of the Igloo is:

$V_{T} = \frac{2}{3}\pi r_{o}^{3} - \frac{2}{3}\pi r_{i}^{3} = \frac{2}{3}\pi [(0.725 m)^{3} - (0.625 m)^{3}] = 0.29 m^{3}$

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

$m = 19.3 \frac{g}{cm^{3}}*0.29 m^{3}*\frac{(100 cm)^{3}}{1 m^{3}} = 5.60 \cdot 10^{6} g$

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

$V = \frac{\ 1263}{oz}*5.60 \cdot 10^{6} g*\frac{1 oz}{31.1034768 g} = \ 227.4 \cdot 10^{6}$  

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

I hope it helps you!