a sheet of metal is 97.4 mm wide and 59.4 mm long. if it weighs 9.788g and the density of the metal is 7.23g/cm^3, what is the thickness of the sheet(in mm) ?
Convert width and length to cm.
Use mass = volume x density and solve for volume.
Volume of sheet metal = length*width*thickness. Substitute for all that applies and solve for thickness.
The thickness will be in cm, convert to mm.
To find the thickness of the sheet, we can use the formula:
Thickness = Mass / (Area x Density)
First, let's calculate the area of the sheet:
Area = Width x Length
Area = 97.4 mm x 59.4 mm
Area = 5785.56 mm^2
Now, substituting the values into the formula:
Thickness = 9.788 g / (5785.56 mm^2 x 7.23 g/cm^3)
Thickness = 9.788 g / (41923.04664 g/mm^3)
Thickness ≈ 0.0002334915 mm
Therefore, the thickness of the sheet is approximately 0.0002334915 mm.
To find the thickness of the sheet, we need to use the formula:
Density = Mass / Volume
First, let's calculate the volume of the sheet. The volume formula is:
Volume = Area × Thickness
We already know the dimensions of the sheet in terms of width and length. Therefore, the area of the sheet can be calculated as:
Area = Width × Length
Let's substitute the given values into the formula:
Area = 97.4 mm × 59.4 mm
Now, we have the formula:
Volume = Area × Thickness
We also know the density of the metal is given as 7.23 g/cm^3, and the mass of the sheet is given as 9.788 g.
Since we want to find the thickness in millimeters, we need to make sure all the measurements are in the same unit. Let's convert the thickness from centimeters to millimeters.
1 cm = 10 mm
Therefore, we can multiply both sides of the equation by 10 mm to convert the units:
Density = 7.23 g / cm^3 × 10 mm / 1 cm
Now, let's simplify the equation:
Density = 72.3 g / mm^3
We can rewrite the volume formula to solve for thickness:
Thickness = Mass / (Density × Area)
Now, we can substitute the given values into the formula:
Thickness = 9.788 g / (72.3 g / mm^3 × 97.4 mm × 59.4 mm)
By performing the calculation, we get the thickness of the sheet in millimeters.