Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a 1ft X 84ft ceiling with gold leaf that is five-millionths of an inch thick. The density of gold is 19.32g/cm^3, and gold costs $ 953 per troy ounce (1 troy ounce = 31.1034768g}). How much will it cost the architect to buy the necessary gold? Express your answer using one significant figures.
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✅ Answers
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Convert all the feet and inches to centimeters and multiply to get the volume of gold
1ft* 30.48cm/1ft=3048 cm
84ft* 30.48cm/1ft=2560.32 cm
5/1in* 2.54cm/1in= 1.27×10^-5cm
3048*2560.32*1.27×10^-5=99.10896cm^3
99.10896cm^3* 19.32g/cm^3=
1914.785g* 1 troy ounce/31.1034768g=61.56177 troy ounces * $953/troy ounce= $58668, $6 for one sigfig
Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a 1ft X 84ft ceiling with gold leaf that is five-millionths of an inch thick. The density of gold is 19.32g/cm^3, and gold costs $ 953 per troy ounce (1 troy ounce = 31.1034768g}). How much will it cost the architect to buy the necessary gold? Express your answer using one significant figures.
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At least attempt some of these problems yourself!
1 ft x 12 in/ft x 2.54 cm/inch = 3049 cm
84 ft x 12 in/ft x 2.54 cm/inch = 2560.3 cm
3049 cm x 2560.3 cm = 793,665 cm^2 area
5 x 10^-6 in x 2.54 in/cm = 1.968 cm^-6. thickness
7.94 x 10^5 cm^2 x 1.968 x 10 -6 cm =
7.94/1.968 x 10^-1 cm^3; = 0.478 cm^3,
and at 19.32 grams/cm^3,
that’s 19.32 g/cm^3 x 0.478 cm^3 = 9.23 grams
of cold. 9.23 grams/ 31.1 grams/Troy oz =
0.2967 troy ox; .2967 troy ox x $ 953/troy oz =
$3.
It is really sad when many students lack the ability for logical thinking…
Oh, wait! If it’s not on a state-mandated test, it must not be important!
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