First, we need to calculate the volume of the gold leaf required to cover the ceiling. The dimensions of the ceiling are 100ft×81ft, and the thickness of the gold leaf is 5×10−6inches.
Convert the dimensions to inches:
- 100ft=100×12=1200inches
- 81ft=81×12=972inches
Calculate the volume in cubic inches:
Volume=1200in×972in×5×10−6in=5.832in3
Convert the volume from cubic inches to cubic centimeters using the conversion 1in3=16.387cm3:
Volume=5.832in3×16.387cm3/in3=95.57cm3
Using the density of gold, 19.32g/cm3, calculate the mass of the gold:
Mass=95.57cm3×19.32g/cm3=1845.2g
Convert the mass from grams to troy ounces using the conversion 1troy ounce=31.10348g:
Mass=31.10348g/troy ounce1845.2g=59.31troy ounces
Calculate the cost of the gold using the price of $1768 per troy ounce:
Cost=59.31troy ounces×1768$/troy ounce=104,800.08$
The cost to cover the ceiling with gold leaf is approximately 100,000$.