Estimate the number of pennies that would fit in a box one foot long by one foot wide by one foot tall. A) 5 × 10² B) 5 × 10³ C) 5 × 10⁴ D) 5 × 10⁵ E) 5 x 10⁶

Question

Quizplus · Accepted Answer

To find the volume of the box in cubic inches, we need to convert the dimensions to inches: 
1 foot = 12 inches

Volume = (12 inches) x (12 inches) x (12 inches) = 1,728 cubic inches

To find the number of pennies that would fit in the box, we need to divide the volume of the box by the volume of one penny. The volume of a penny can be approximated as the volume of a cylinder with a diameter of 0.75 inches and a thickness of 0.06 inches.

Volume of a penny = πr^2h = π(0.375 inches)^2(0.06 inches) = 0.0212 cubic inches

Number of pennies = (Volume of box) / (Volume of penny) = 1,728 cubic inches / 0.0212 cubic inches/penny = 81,509 pennies

Since there are likely to be small gaps between the pennies when stacked, we can round down to the nearest thousand, giving us an estimate of 81,000 pennies.

The closest answer choice is C, which is 5 x 10^14 pennies, or 50 trillion pennies.

Estimate the Number of Pennies That Would Fit in a Box