Estimate the number of pennies that would fit in a box one foot long by one foot wide by one foot tall. A) 5 × 10^2 B) 5 × 10^3 C) 5 × 10^4 D) 5 × 10^5 E) 5 x 10^6
Answer
Estimating the Number of Pennies in a 1-Foot Cubic Box
To estimate how many U.S. pennies can fit inside a box measuring 1 ft × 1 ft × 1 ft, we need to compare the volume of the box with the volume of a single penny.
📏 Step 1: Volume of the Box
1 foot = 12 inches
Volume = 12 in × 12 in × 12 in = 1,728 in³
Volume = 12 in × 12 in × 12 in = 1,728 in³
🪙 Step 2: Volume of One Penny
- Diameter ≈ 0.75 inches
- Thickness ≈ 0.06 inches
Volume of a penny (approximated as a cylinder):
V = π × r² × h ≈ 3.14 × (0.375)² × 0.06 ≈ 0.0265 in³
V = π × r² × h ≈ 3.14 × (0.375)² × 0.06 ≈ 0.0265 in³
🧮 Step 3: Estimating Number of Pennies
Number of pennies ≈ Box volume / Penny volume
≈ 1,728 in³ / 0.0265 in³ ≈ 65,207
≈ 1,728 in³ / 0.0265 in³ ≈ 65,207
🎯 Final Estimate and Closest Option
The closest scientific notation match is:
6.5 × 10⁴ ≈ 5 × 10⁴ → Answer: C)
📝 Conclusion
Based on volume approximation, approximately 65,000 pennies can fit in a 1 cubic foot box, making the best answer choice 5 × 10⁴.