A 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

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To calculate the length of the square brass plate in centimeters, you need to find the volume and the height of the plate.

1. Calculate the volume:
Given that the density of the brass is 8.4 g/cm³ and the mass of the plate is 1.05 kg, we need to convert the mass to grams for consistency.
1 kg = 1000 g
Therefore, the mass of the plate is 1.05 kg × 1000 g = 1050 g.

Now, we can use the formula:
Density = Mass / Volume

Rearranging the formula to solve for volume:
Volume = Mass / Density

The volume of the brass plate will be:
Volume = 1050 g / 8.4 g/cm³

2. Calculate the height:
The height of the brass plate is given as 2 mm. However, to be consistent with the units used in the density, we need to convert it to centimeters.
1 cm = 10 mm
Therefore, the height of the brass plate is 2 mm / 10 mm/cm = 0.2 cm.

3. Calculate the length:
To calculate the length, we can use the formula for the volume of a rectangular solid:
Volume = Length × Width × Height

Since the plate is square, the length and width are the same. Let's call this value "x" cm.

Substituting the values into the formula:
1050 g / 8.4 g/cm³ = x cm × x cm × 0.2 cm

Simplifying the equation:
1050 g / 8.4 g/cm³ = 0.2 x² cm³

Rearranging the equation to solve for x:
x² = (1050 g / 8.4 g/cm³) / 0.2 cm³

Calculating the value of x:
x² = 625 cm²

Taking the square root of both sides:
x = √625 cm²

Simplifying:
x = 25 cm

Therefore, the length of the square brass plate is 25 centimeters.