Gold can be hammered into extremely thin sheets called gold leaf. an architect wants to cover a 100 ftã 89 ft ceiling with gold leaf that is five-millionths of an inch thick. the density of gold is 19.32 g/cm3, and gold costs $ 953 per troy ounce (1 troy ounce = 31.1034768 g). how much will it cost the architect to buy the necessary gold?

$62160.534

Explanation:

If the architect needs to cover a 100 ft x 89 ft ceiling with gold leaf sheets with a thickness of , he will need  to cover a volume  as follows (assuming the ceiling has a rectangular shape):

(1)

Where:

Then: (2)

On the other hand, density is defined as the relation between the mass of an object and its volume :

(3)

As we know the density of gold is and the volume the architect needs to cover, we can find the mass.

(4)

But first, we have to change the dimensions of the volume we calculated, in order to work with the same units:

Substituting in (4):

(5)

(6) This is the amount of gold keaf sheets the architect needs.

Now, if we know cost $ 953, we can find how much of gold cost:

Therefore, the architect will need $62160.534 to buy the necessary gold to cover the ceiling.

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