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.
the plate has a volume of
(1050g)/(8.4 g/cm^3) = 125 cm^3
Since v = s^2 * h,
.2s^2 = 125
s^2 = 625
s = 25 cm
Please explain clearly
Susan
Mwaniki
Pls explain clearly
mass=1.05kg density=8.4g/cm^3 volume=mass/density convert 1.05kg to grams to be=1050g take volume=1050g/8.4g/cm=125 cm so volume =125 .1.05kg=2mm what about 8mm to get 8mm to be 5 kg so 125 *5=625 . lengh of squar is squareroot of 625 to get is 25cm
To calculate the length of the brass plate, we need to use the formula:
Density = mass / volume
First, let's find the volume of the brass plate. We know that the thickness of the plate is 2 mm. Since it's a square plate, all sides will have the same length.
Let's assume the length of each side of the square plate is 'l' cm.
The volume of a rectangular prism (which a square plate is) is given by the formula:
Volume = length x width x height
In this case, since it's a square plate, the length and width are the same. So, the formula becomes:
Volume = l x l x 2 mm
Remember that we need the volume in cm³, so we need to convert the thickness from mm to cm:
Thickness in cm = 2 mm / 10 = 0.2 cm
Now, we can rewrite the volume equation:
Volume = l x l x 0.2 cm
Next, we substitute the given values into the density equation:
8.4 g/cm³ = 1.05 kg / Volume
To find the volume, we rearrange the equation:
Volume = 1.05 kg / 8.4 g/cm³
Since we want the length in centimeters, we need to find the volume in cm³ per cm². So, we divide the volume by the area (l x l) of the plate:
Volume / Area = (1.05 kg / 8.4 g/cm³) / (l x l)
To simplify, we convert the mass to grams:
Volume / Area = (1050 g / 8.4 g/cm³) / (l x l)
Now, we can calculate the volume per unit area:
Volume / Area = 125 cm³/cm² / (l x l)
Finally, we can isolate 'l' by dividing both sides by (125 cm³/cm²):
l x l = 125 cm³/cm² / (Volume / Area)
l x l = (125 cm³/cm²) x (Area / Volume)
We know that the area (A) of a square is:
Area = length x width
In this case, since it's a square plate, the length and width are the same. So, the formula becomes:
Area = l x l
Now we can substitute this value in:
l x l = (125 cm³/cm²) x (l x l) / Volume
Simplifying:
l x l = 125 cm³/cm² x 1 / Volume
l x l = 125 cm³/cm² / Volume
Dividing by l x l on both sides:
l x l / l x l = 1 / (125 cm³/cm² / Volume)
1 = 1 / (125 cm³/cm² / Volume)
1 = Volume / 125 cm³/cm²
To find l, we take the square root of both sides:
l = √(Volume / 125 cm³/cm²)
Now we can substitute the known values:
l = √(Volume / 125 cm³/cm²)
l = √((1.05 kg / 8.4 g/cm³) / 125 cm³/cm²)
l = √(1.05 kg / (8.4 g/cm³ x 125 cm³/cm²))
Now we can calculate the length of the plate by substituting the values and simplifying:
l = √(1.05 kg / (8.4 g/cm³ x 125 cm³/cm²))
l ≈ √(0.011964 cm)
l ≈ 0.1095 cm
Therefore, the length of the square brass plate is approximately 0.1095 cm.