square brass plate is 2 mm thick and has a mass of 1.05 kg. The density of the brass is 8.4 g/cm3. Calculate the length of the plate in centimeters
To calculate the length of the brass plate, we need to find the volume first.
The formula for volume (V) is:
V = mass / density
Given that the mass of the brass plate is 1.05 kg and the density of brass is 8.4 g/cm^3, we need to convert the mass to grams:
mass = 1.05 kg * 1000 g/kg = 1050 g
Now let's plug these values into the formula to find the volume:
V = 1050 g / 8.4 g/cm^3
V ≈ 125 cm^3
Since the brass plate is square, the volume can also be calculated by multiplying the area of the base (length * width) by the thickness.
The formula for volume in terms of length (L) and thickness (T) is:
V = L * L * T
Now we can solve for the length (L):
L * L * 2 mm = 125 cm^3
First, convert the thickness from millimeters to centimeters:
2 mm = 0.2 cm
Now we have:
L * L * 0.2 cm = 125 cm^3
Simplifying this equation, we have:
L^2 = 125 cm^3 / 0.2 cm
L^2 ≈ 625 cm^2
To find L, we need to take the square root of both sides:
L ≈ sqrt(625) cm
L ≈ 25 cm
Therefore, the length of the brass plate is approximately 25 centimeters.