A flat circular plate of copper has a radius of 0.278 m and a mass of 42.6 kg. What is the thickness of the plate? answer in units of m
To find the thickness of the plate, we can use the formula for the volume of a cylinder which is given by:
Volume = π * r² * h,
where "r" is the radius of the plate and "h" is the height (thickness) of the plate.
Given that the plate is flat and circular, we can assume that the thickness is the height of the cylinder.
Given:
Radius (r) = 0.278 m
Mass = 42.6 kg
First, let's calculate the volume of the plate using the formula:
Volume = π * r² * h
We know that the mass of the plate is directly proportional to its volume, so we can use the density formula:
Density = Mass / Volume
The density of copper is approximately 8,960 kg/m³.
Plugging in the given values, we have:
8,960 kg/m³ = 42.6 kg / (π * 0.278² * h)
Now, let's solve this equation to find the thickness (h) of the plate:
h = 42.6 kg / (π * 0.278² * 8,960 kg/m³)
By evaluating the expression on the right side of the equation, we can determine the thickness of the plate.
Let's calculate the thickness using a calculator:
h ≈ 42.6 / (π * 0.278² * 8960)
h ≈ 42.6 / (π * 0.077284 * 8960)
h ≈ 42.6 / (220.4950464)
h ≈ 0.193 m
Therefore, the thickness of the plate is approximately 0.193 meters.