To find the thickness of the glass, we need to use the formula for the volume of a rectangular prism:
Volume = length × width × height
In this case, the length is 8.5 inches, the width is 6.75 inches, and the height is 2.5 inches. Converting these measurements to centimeters (since the density is given in grams per cubic centimeter), we get:
Length = 8.5 inches × 2.54 cm/inch = 21.59 cm
Width = 6.75 inches × 2.54 cm/inch = 17.15 cm
Height = 2.5 inches × 2.54 cm/inch = 6.35 cm
Now we can calculate the volume of the dish:
Volume = length × width × height
Volume = 21.59 cm × 17.15 cm × 6.35 cm
Volume = 2383.6 cm^3
Next, we can use the density of the glass to calculate the mass of the glass:
Density = mass / volume
mass = density × volume
mass = 2.23 g/cm^3 × 2383.6 cm^3
mass = 5322.428 g or 5.322428 kg
Now we can calculate the mass of the glass alone by subtracting the mass of the dish:
mass of glass = 5.322428 kg - 0.9 kg
mass of glass = 4.422428 kg
Finally, we can use the formula for the volume of a cylinder to find the thickness of the glass:
Volume = π × r^2 × h
where r is the radius of the dish and h is the thickness of the glass.
We can calculate the radius of the dish by dividing the width and length by 2:
radius = width / 2 = 6.75 inches / 2 × 2.54 cm/inch = 8.575 cm
radius = length / 2 = 8.5 inches / 2 × 2.54 cm/inch = 10.795 cm
Taking the average of these two values, we get:
radius = (8.575 cm + 10.795 cm) / 2 = 9.685 cm
Now we can solve for the thickness of the glass:
Volume = π × r^2 × h
h = Volume / (π × r^2)
h = 2383.