Final answer:
To find the average thickness of the gold leaf sheet, first calculate the width by dividing the area by the length. Then, calculate the radius of the gold piece using the width. Next, find the volume of the gold piece by dividing the mass by the density. Finally, calculate the thickness by dividing the volume by the length of the sheet and convert it from millimeters to meters.
Step-by-step explanation:
To find the average thickness of the gold leaf sheet, we need to use the formula for volume of a cylinder: V = πr^2h, where r is the radius and h is the height (thickness). We are given the length and width of the sheet, so we can divide the area of the sheet by the length to find the width. Then, we can calculate the radius using the formula r = width/2. Once we know the radius and density of gold, we can find the volume of the gold piece and then divide it by the length of the sheet to find the average thickness. Finally, we convert the thickness from millimeters to meters by dividing it by 1000.
Step-by-step solution:
- Calculate the width of the sheet by dividing the area by the length: width = area/length
- Calculate the radius: r = width/2
- Calculate the volume of the gold: V = mass/density
- Calculate the thickness: thickness = V/length
- Convert the thickness from millimeters to meters: thickness = thickness/1000