Let's break down the problem step-by-step.
Given:
- Number of sheets = 500
- Mass of 1.0 m² of paper = 0.080 kg
- Length of one sheet = 0.300 m
- Width of one sheet = 0.210 m
- Height of pile of 500 sheets = 0.048 m
Step 1: Calculate the area of one sheet of paper.
The area (A) of a rectangle is given by:
A = length × width = 0.300 m × 0.210 m = 0.063 m²
Step 2: Calculate the mass of one sheet of paper.
Since 1.0 m² of paper weighs 0.080 kg, the mass of one sheet with an area of 0.063 m² is:
Mass = area × mass per m² = 0.063 m² × 0.080 kg/m² = 0.00504 kg
So, one sheet weighs approximately 0.00504 kg (or 5.04 grams).
Step 3: Calculate the volume of the pile of 500 sheets.
The pile forms a rectangular block with:
- length = 0.300 m
- width = 0.210 m
- height = 0.048 m
Volume (V) is:
V = length × width × height = 0.300 m × 0.210 m × 0.048 m = 0.003024 m³
Step 4: Calculate the total mass of the 500 sheets.
Mass of one sheet is 0.00504 kg, so total mass is:
Total mass = 500 × 0.00504 kg = 2.52 kg
Step 5: Calculate the density of the paper.
Density (ρ) is mass divided by volume:
ρ = mass / volume = 2.52 kg / 0.003024 m³ ≈ 833.33 kg/m³
This means the density of the paper is approximately 833 kg/m³.
Summary:
- Mass of one sheet ≈ 0.00504 kg (5.04 grams)
- Density of paper ≈ 833 kg/m³
If you have any questions, feel free to ask!