What will be the difference in mass (in g) between two packets each containing 500 sheets of 80 GSM and 70 GSM papers of size 20 cm × 30 cm? (GSM = g/m2)
Paper Mass Difference Calculation
This question asks for the difference in mass between two packets of paper, each containing the same number of sheets but with different paper densities (GSM).
We are given the following information:
- Number of sheets per packet = 500
- Size of each sheet = 20 cm $\times$ 30 cm
- Packet 1 paper density = 80 GSM (g/m²)
- Packet 2 paper density = 70 GSM (g/m²)
We need to find the difference in total mass (in grams) between the two packets.
Paper Area Calculation
First, let's calculate the area of one sheet of paper. The dimensions are given in centimeters (cm), and the GSM is given in grams per square meter (g/m²), so we need to convert the dimensions to meters (m).
- Length = 30 cm = $\frac{30}{100}$ m = 0.3 m
- Width = 20 cm = $\frac{20}{100}$ m = 0.2 m
The area of one sheet is:
\( \text{Area} = \text{Length} \times \text{Width} \)
\( \text{Area} = 0.3 \, \text{m} \times 0.2 \, \text{m} = 0.06 \, \text{m}^2 \)
Mass per Sheet Calculation
GSM (Grams per Square Meter) tells us the mass of one square meter of paper. To find the mass of one sheet, we multiply the GSM by the area of the sheet in square meters.
\( \text{Mass per sheet} = \text{GSM} \times \text{Area per sheet} \)
- Mass of one 80 GSM sheet: \( 80 \, \text{g/m}^2 \times 0.06 \, \text{m}^2 = 4.8 \, \text{g} \)
- Mass of one 70 GSM sheet: \( 70 \, \text{g/m}^2 \times 0.06 \, \text{m}^2 = 4.2 \, \text{g} \)
Total Mass Calculation for each Packet
Each packet contains 500 sheets. To find the total mass of each packet, we multiply the mass per sheet by the number of sheets.
- Total mass of the 80 GSM packet: \( 500 \, \text{sheets} \times 4.8 \, \text{g/sheet} = 2400 \, \text{g} \)
- Total mass of the 70 GSM packet: \( 500 \, \text{sheets} \times 4.2 \, \text{g/sheet} = 2100 \, \text{g} \)
Mass Difference Calculation
Finally, to find the difference in mass between the two packets, we subtract the mass of the lighter packet from the mass of the heavier packet.
\( \text{Mass Difference} = \text{Total mass of 80 GSM packet} - \text{Total mass of 70 GSM packet} \)
\( \text{Mass Difference} = 2400 \, \text{g} - 2100 \, \text{g} = 300 \, \text{g} \)
The difference in mass between the two packets is 300 g.
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