can someone explain to me how to answer this:
Polycarbonate plastic has a density of 1.2 g/c3. A photo frame is constructed from two 3.0 mm sheets of polycarbonate. Each sheet measures 28 cm by 22cm.What is the mass of the photo frame?
Well, if I were to frame this question with a funny twist, I'd say the photo frame is going to weigh as much as two singing elephants wearing polycarbonate costumes doing a tap dance! But let's calculate it for real this time.
To find the mass of the photo frame, we need to first calculate the volume of the polycarbonate used, and then multiply it by the density of polycarbonate.
The volume (V) of each sheet can be calculated by multiplying the length (L), width (W), and thickness (T) together:
V = L x W x T
Using the given measurements, the volume of each sheet is:
V = 0.28 m x 0.22 m x 0.003 m
Since there are two sheets, we can double the volume:
Total volume = 2 x (0.28 m x 0.22 m x 0.003 m)
Now, we can calculate the mass (M) of the frame using the density of polycarbonate (D):
M = V x D
Given that the density of polycarbonate is 1.2 g/cm³, we need to convert the volume from cubic meters to cubic centimeters (cm³) and adjust the units accordingly:
Total mass = (Total volume in cm³) x 1.2 g/cm³
Once the units are adjusted, multiply by the density and there you have it, the mass of your photo frame! I'm sure it'll be a weighty subject of conversation at your next family gathering.
To calculate the mass of the photo frame, you need to determine the volume of the polycarbonate sheets first, and then multiply it by the density.
Step 1: Calculate the volume of one polycarbonate sheet.
The thickness of each sheet is given as 3.0 mm. Since density is mass/volume, we need to convert this thickness from millimeters to centimeters, so the units match the density (g/cm^3).
Volume of one sheet = length × width × thickness = 28 cm × 22 cm × 0.3 cm.
Step 2: Calculate the total volume of the two polycarbonate sheets.
Since there are two identical sheets, we can multiply the volume of one sheet by 2.
Total volume of both sheets = 2 × (28 cm × 22 cm × 0.3 cm).
Step 3: Calculate the mass of the photo frame.
Mass = density × volume.
Mass = 1.2 g/cm^3 × total volume of both sheets.
Now, you can substitute the values and calculate the mass.
To answer this question, we need to follow a few steps:
Step 1: Find the volume of one sheet of polycarbonate.
Since each sheet of polycarbonate measures 28 cm by 22 cm, we can calculate the area of one sheet by multiplying the length and width:
Area of one sheet = 28 cm * 22 cm
Step 2: Convert the area from square centimeters to square meters.
To convert from square centimeters to square meters, we divide the area by 10,000 since there are 10,000 square centimeters in a square meter:
Area of one sheet in square meters = (28 cm * 22 cm) / 10,000
Step 3: Calculate the volume of one sheet.
Since the thickness of each sheet is given as 3.0 mm, we need to convert it to meters to have the same unit as the area:
Thickness of one sheet in meters = 3.0 mm / 1,000
Then, we can calculate the volume of one sheet by multiplying the area by the thickness:
Volume of one sheet = Area of one sheet in square meters * Thickness of one sheet in meters
Step 4: Calculate the total volume of the photo frame.
Since the photo frame is constructed using two sheets of polycarbonate, we need to double the volume calculated in step 3 to get the total volume:
Total volume of the photo frame = 2 * Volume of one sheet
Step 5: Calculate the mass of the photo frame.
The density of polycarbonate is given as 1.2 g/cm^3. Since the total volume of the photo frame is in cubic meters, we need to convert the density to match this unit. Therefore, we divide the density by 1,000 to convert it to g/m^3:
Density of polycarbonate in g/m^3 = 1.2 g/cm^3 / 1,000
Finally, we can calculate the mass of the photo frame by multiplying the density by the total volume:
Mass of the photo frame = Total volume of the photo frame * Density of polycarbonate in g/m^3
By following these steps and plugging in the given values, we can find the mass of the photo frame.
Mass = Volume x density
= 28x22x6 cm^3 x 1.2 g/cm^3
The answer will be in grams. Divide it by 1000 for kilograms