What is the best estimate of the mass of a pencil.
The correct answer and explanation is:
Best estimate of the mass of a pencil:
About 5 to 10 grams
Explanation:
When estimating the mass of everyday objects like a pencil, it helps to think about its size, materials, and typical uses. A standard wooden pencil is usually about 7 inches (17.5 cm) long, cylindrical with a diameter roughly 7 mm. Most pencils are made of a combination of wood, graphite (the “lead”), and a small metal ferrule holding an eraser.
Why 5 to 10 grams?
- Material density: Wood used in pencils is generally lightweight. Wood density varies but is roughly 0.6 to 0.8 g/cm³. The graphite core is denser, around 2.2 g/cm³, but the core is very thin.
- Volume considerations: The total volume of a pencil is small, on the order of a few cubic centimeters. For example, a 17.5 cm pencil with a 0.7 cm diameter has a volume roughly: Volume≈π×(0.35 cm)2×17.5 cm≈6.7 cm3\text{Volume} \approx \pi \times (0.35\, \text{cm})^2 \times 17.5\, \text{cm} \approx 6.7\, \text{cm}^3 Multiplying volume by density (using 0.7 g/cm³ for wood as an average) gives roughly: 6.7 cm3×0.7 g/cm3=4.7 g6.7\, \text{cm}^3 \times 0.7\, \text{g/cm}^3 = 4.7\, \text{g} Adding the graphite core and eraser might add a couple more grams.
Practical measurements:
If you have a kitchen scale, you can weigh a pencil directly and expect a mass near this range. Different types of pencils (e.g., mechanical pencils with metal parts) can weigh more, but a traditional wooden pencil usually falls between 5 and 10 grams.
Comparison to other objects:
- A US penny weighs about 2.5 grams, so a pencil is roughly twice to four times the weight of a penny.
- A typical smartphone weighs around 150 grams, making the pencil much lighter.
Why estimate instead of exact?
Pencils vary in size and composition, so the mass can differ slightly. However, 5–10 grams is a reliable estimate that reflects the typical pencil most people use in schools or offices.
In summary, the best estimate for the mass of a standard wooden pencil is around 5 to 10 grams, based on its size, materials, and practical measurements.